00645nas a2200205 4500008004100000022001400041245007800055210006900133300000900202490000600211653001900217653002000236653002400256653001500280653001900295100001900314700002000333700002300353856006300376 2022 eng d a2640-350100aLong-time stability of the quantum hydrodynamic system on irrational tori0 aLongtime stability of the quantum hydrodynamic system on irratio a1-240 v410aEuler-Korteweg10airrational tori10along time stability10aQHD system10aSmall divisors1 aFeola, Roberto1 aIandoli, Felice1 aMurgante, Federico uhttps://www.aimspress.com/article/doi/10.3934/mine.202202300623nas a2200133 4500008004100000245014300041210006900184100002200253700002300275700002400298700001600322700002100338856013000359 2021 eng d00aConsistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows0 aConsistency of the full and reduced order models for EvolveFilte1 aStrazzullo, Maria1 aGirfoglio, Michele1 aBallarin, Francesco1 aIliescu, T.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/consistency-full-and-reduced-order-models-evolve-filter-relax-regularization-convection00750nas a2200217 4500008004100000245007000041210006800111300001600179490000700195100002300202700002400225700002400249700002400273700002300297700002100320700002100341700002200362700002000384700002400404856010400428 2021 eng d00aNon-intrusive data-driven ROM framework for hemodynamics problems0 aNonintrusive datadriven ROM framework for hemodynamics problems a1183–11910 v371 aGirfoglio, Michele1 aScandurra, Leonardo1 aBallarin, Francesco1 aInfantino, Giuseppe1 aNicolò, Francesca1 aMontalto, Andrea1 aRozza, Gianluigi1 aScrofani, Roberto1 aComisso, Marina1 aMusumeci, Francesco uhttps://www.math.sissa.it/publication/non-intrusive-data-driven-rom-framework-hemodynamics-problems01167nas a2200217 4500008004100000022001400041245008300055210006900138300001400207490000700221520048300228653002500711653001800736653002400754653000800778653003100786653002200817100001900839700002000858856007100878 2019 eng d a0294-144900aLocal well-posedness for quasi-linear NLS with large Cauchy data on the circle0 aLocal wellposedness for quasilinear NLS with large Cauchy data o a119 - 1640 v363 a

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

10aDispersive equations10aEnergy method10aLocal wellposedness10aNLS10aPara-differential calculus10aQuasi-linear PDEs1 aFeola, Roberto1 aIandoli, Felice uhttp://www.sciencedirect.com/science/article/pii/S029414491830042801187nas a2200133 4500008004100000022001400041245009900055210007100154260000800225520074000233100002000973700001300993856004701006 2019 eng d a1432-091600aTwo-Dimensional Yang–Mills Theory on Surfaces with Corners in Batalin–Vilkovisky Formalism0 aTwoDimensional Yang–Mills Theory on Surfaces with Corners in Bat cMar3 a

In this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang–Mills theory.

1 aIraso, Riccardo1 aMnev, P. uhttps://doi.org/10.1007/s00220-019-03392-w00439nas a2200097 4500008004100000245008500041210006900126100001900195700002000214856010700234 2018 eng d00aLong time existence for fully nonlinear NLS with small Cauchy data on the circle0 aLong time existence for fully nonlinear NLS with small Cauchy da1 aRoberto, Feola1 aIandoli, Felice uhttps://www.math.sissa.it/publication/long-time-existence-fully-nonlinear-nls-small-cauchy-data-circle00359nas a2200121 4500008004100000245004300041210004200084100001600126700001900142700002000161700001900181856003700200 2018 eng d00aObservables in the equivariant A-model0 aObservables in the equivariant Amodel1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo1 aZabzine, Maxim uhttps://arxiv.org/abs/1807.0865901416nas a2200169 4500008004100000020002200041245008400063210007000147260004400217300001400261520082100275100002001096700002301116700002901139700002901168856004901197 2017 eng d a978-3-319-58904-600aDispersive Estimates for Schrödinger Operators with Point Interactions in ℝ30 aDispersive Estimates for Schrödinger Operators with Point Intera aChambSpringer International Publishing a187–1993 a

The study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

1 aIandoli, Felice1 aScandone, Raffaele1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1100704nas a2200181 4500008004100000245009900041210006900140300001400209490000700223100001700230700002000247700002000267700002200287700002100309700002000330700002200350856015000372 2017 eng d00aNumerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts0 aNumerical modeling of hemodynamics scenarios of patientspecific  a1373-13990 v161 aBallarin, F.1 aFaggiano, Elena1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aIppolito, Sonia1 aScrofani, Roberto uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd000889nas a2200169 4500008004100000022001400041245004700055210004600102260000800148300000800156490000900164520044700173100001600620700001900636700002000655856004400675 2016 eng d a1029-847900aComparing Poisson Sigma Model with A-model0 aComparing Poisson Sigma Model with Amodel cOct a1330 v20163 a

We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo uhttps://doi.org/10.1007/JHEP10(2016)13301710nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100001701305700002001322700002001342700002101362700002201383700002001405700002201425700001801447856005101465 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.1 aBallarin, F.1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524001905nas a2200157 4500008004100000245012000041210006900161260002200230300000800252490000700260520128900267100002101556700002201577700002101599856012701620 2016 en d00aReduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries0 aReduced basis method and domain decomposition for elliptic probl bElsevierc01/2016 a4300 v713 aThe aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.1 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-method-and-domain-decomposition-elliptic-problems-networks-and-complex01813nas a2200169 4500008004100000245015600041210006900197520118400266100001701450700002001467700002001487700002001507700002201527700002101549700002201570856005101592 2015 en d00aFast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization0 aFast simulations of patientspecific haemodynamics of coronary ar3 aIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.1 aBallarin, F.1 aFaggiano, Elena1 aIppolito, Sonia1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aScrofani, Roberto uhttp://urania.sissa.it/xmlui/handle/1963/3462300921nas a2200109 4500008004100000245010000041210006900141260001300210520051500223100002200738856005100760 2014 en d00aA density result for GSBD and its application to the approximation of brittle fracture energies0 adensity result for GSBD and its application to the approximation bSpringer3 a

We present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

1 aIurlano, Flaviana uhttp://urania.sissa.it/xmlui/handle/1963/3464701082nas a2200145 4500008004100000245007200041210006900113300001400182490000800196520057300204100001600777700002100793700002100814856010100835 2014 eng d00aAn improvement on geometrical parameterizations by transfinite maps0 aimprovement on geometrical parameterizations by transfinite maps a263–2680 v3523 aWe present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.1 aJäggli, C.1 aIapichino, Laura1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/improvement-geometrical-parameterizations-transfinite-maps00566nas a2200133 4500008004100000245010000041210006900141300001000210100002100220700002200241700002100263700002100284856012700305 2014 eng d00aReduced basis method for the Stokes equations in decomposable domains using greedy optimization0 aReduced basis method for the Stokes equations in decomposable do a1–71 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aVolkwein, Stefan uhttps://www.math.sissa.it/publication/reduced-basis-method-stokes-equations-decomposable-domains-using-greedy-optimization01521nas a2200133 4500008004100000245009100041210006900132260001000201520106100211653003701272100002001309700002201329856003601351 2013 en d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in  bSISSA3 a

We provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/661500531nas a2200109 4500008004100000245011300041210006900154260001000223653003700233100002200270856012900292 2013 en d00aAn Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems0 aApproximation Result for Generalised Functions of Bounded Deform bSISSA10aFunctions of bounded deformation1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/approximation-result-generalised-functions-bounded-deformation-and-applications-damage01988nas a2200133 4500008004100000245010500041210006900146260003000215520151100245100002101756700002201777700001901799856003601818 2013 en d00aEarly phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus0 aEarly phase of plasticityrelated gene regulation and SRF depende bPublic Library of Science3 aHippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.1 aIacono, Giovanni1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/728700902nas a2200121 4500008004100000245005300041210005200094260004800146520050700194100002100701700002200722856003600744 2013 en d00aFracture models as Gamma-limits of damage models0 aFracture models as Gammalimits of damage models bAmerican Institute of Mathematical Sciences3 a

We analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

1 aDal Maso, Gianni1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/422501414nas a2200145 4500008004100000245008300041210006900124260002800193520092600221100002001147700002201167700002101189700002201210856003601232 2012 en d00aDecompositions of large-scale biological systems based on dynamical properties0 aDecompositions of largescale biological systems based on dynamic bOxford University Press3 aMOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article.1 aSoranzo, Nicola1 aRamezani, Fahimeh1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/522601741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650401286nas a2200145 4500008004100000245007900041210006900120260003300189520078400222653003101006100002401037700002101061700002201082856003601104 2011 en d00aComputing global structural balance in large-scale signed social networks.0 aComputing global structural balance in largescale signed social  bNational Academy of Sciences3 aStructural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"10aCombinatorial optimization1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/642600878nas a2200109 4500008004100000245008900041210006900130260002200199520048900221100002200710856003600732 2011 en d00aFracture and plastic models as Gamma-limits of damage models under different regimes0 aFracture and plastic models as Gammalimits of damage models unde bWalter de Gruyter3 a

We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/506902106nas a2200121 4500008004300000245013400043210006900177260001900246520164000265100002101905700002201926856003601948 2010 en_Ud 00aMonotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks0 aMonotonicity frustration and ordered response an analysis of the bBioMed Central3 aBackground. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/405500369nas a2200085 4500008004100000245006200041210006200103100002200165856009600187 2010 eng d00aNew approximation results for free discontinuity problems0 aNew approximation results for free discontinuity problems1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/new-approximation-results-free-discontinuity-problems00857nas a2200133 4500008004100000245010700041210007200148300001200220490000700232520040100239100002000640700001700660856004600677 2009 eng d00aSolutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions0 aSolutions of the Schrödinger–Poisson problem concentrating on sp a707-7200 v193 a

In this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

1 aIanni, Isabella1 aVaira, Giusi uhttps://doi.org/10.1142/S021820250900358900915nas a2200145 4500008004100000245009900041210007000140260003700210300001400247490000600261520034300267100002000610700001700630856012200647 2008 eng d00aOn concentration of positive bound states for the Schrödinger-Poisson problem with potentials0 aconcentration of positive bound states for the SchrödingerPoisso bAdvanced Nonlinear Studies, Inc. a573–5950 v83 a

We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

1 aIanni, Isabella1 aVaira, Giusi uhttps://www.math.sissa.it/publication/concentration-positive-bound-states-schr%C3%B6dinger-poisson-problem-potentials