00467nas a2200121   4500008004100000245010400041210006900145260001900214100002900233700002600262700002100288856003600309       2011                        en  d00aOn the number of eigenvalues of a model operator related to a system of three particles on lattices0 anumber of eigenvalues of a model operator related to a system of  bIOP Publishing1 aDell'Antonio, Gianfausto1 aMuminov, Zahriddin I.1 aShermatova, Y.M.  uhttp://hdl.handle.net/1963/549601687nas a2200121   4500008004300000245008300043210007000126520125600196100002201452700002901474700002601503856003601529       2007                        en_Ud  00aThe number of eigenvalues of three-particle Schrödinger operators on lattices0 anumber of eigenvalues of threeparticle Schrödinger operators on 3 aWe consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.1 aAlbeverio, Sergio1 aDell'Antonio, Gianfausto1 aLakaev, Saidakhmat N.  uhttp://hdl.handle.net/1963/257600455nas a2200109   4500008004100000245012600041210006900167260001800236100002900254700002700283856003500310       1989                        en  d00aOn the number of families of periodic solutions of a Hamiltonian system near equilibrium. II.  (English. Italian summary)0 anumber of families of periodic solutions of a Hamiltonian system  bSISSA Library1 aDell'Antonio, Gianfausto1 aD'Onofrio, Biancamaria  uhttp://hdl.handle.net/1963/609