@article {2021, title = {On Dini derivatives of real functions}, year = {2021}, author = {Giuliano Klun and Alessandro Fonda and Andrea Sfecci} } @article {2021, title = {Non-well-ordered lower and upper solutions for semilinear systems of PDEs}, journal = {Communications in Contemporary MathematicsCommunications in Contemporary Mathematics}, year = {2021}, month = {2021/08/27}, pages = {2150080}, abstract = {

We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.

}, isbn = {0219-1997}, url = {https://doi.org/10.1142/S0219199721500802}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2021, title = {Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces}, volume = {18}, year = {2021}, month = {2021/09/07}, pages = {223}, abstract = {

We prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations.

}, isbn = {1660-5454}, url = {https://doi.org/10.1007/s00009-021-01857-8}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2021, title = {Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems}, journal = {Advanced Nonlinear Studies}, volume = {21}, year = {2021}, month = {2021}, pages = {397 - 419}, url = {https://doi.org/10.1515/ans-2021-2117}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2020, title = {On functions having coincident p-norms}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, volume = {199}, year = {2020}, pages = {955-968}, abstract = {

In a measure space $(X,{\mathcal {A}},\mu )$, we consider two measurable functions $f,g:E\rightarrow {\mathbb {R}}$, for some $E\in {\mathcal {A}}$. We prove that the property of having equal p-norms when p varies in some infinite set $P\subseteq [1,+\infty )$ is equivalent to the following condition: $\begin{aligned} \mu (\{x\in E:|f(x)|\>\alpha \})=\mu (\{x\in E:|g(x)|\>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

}, doi = {10.1007/s10231-019-00907-z}, url = {https://doi.org/10.1007/s10231-019-00907-z}, author = {Giuliano Klun} } @article {2020, title = {Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori}, journal = {NONLINEAR ANALYSIS}, year = {2020}, abstract = {

We prove the existence of periodic solutions of some infinite-dimensional nearly integrable Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization of the Poincar{\'e}{\textendash}Birkhoff Theorem.

}, issn = {0362-546X}, doi = {10.1016/j.na.2019.111720}, url = {https://doi.org/10.1016/j.na.2019.111720}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2019, title = {On the topological degree of planar maps avoiding normal cones}, journal = {TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS}, volume = {53}, number = {SISSA;04/2019/MATE}, year = {2019}, pages = {825-845}, publisher = {SISSA}, abstract = {

The classical Poincar{\'e}-Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones.
We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than $1$.

}, issn = {1230-3429}, doi = {10.12775/TMNA.2019.034}, url = {http://dx.doi.org/10.12775/TMNA.2019.034}, author = {Alessandro Fonda and Giuliano Klun} } @article {2015, title = {Gli abachi: antichi strumenti precursori delle moderne macchine da calcolo}, year = {2015}, url = {http://hdl.handle.net/10077/10884}, author = {Giuliano Klun} }