Multiple and least energy sign-changing solutions for Schrodinger-Poisson equations in R3 with restraint

In this paper, we study the existence of multiple sign-changing solutions with a prescribed Lp+1−norm and theexistence of least energy sign-changing restrained solutions for the following nonlinear Schr¨odinger-Poisson system:By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow,we prove that this system has infinitely many sign-changing solutions with the prescribed Lp+1−norm and has a least energy forsuch sign-changing restrained solution for p ∈ (3, 5). Few existence results of multiple sign-changing restrained solutions areavailable in the literature. Our work generalize some results in literature

Statistical mechanics of general discrete nonlinear Schr{\"o}dinger models: Localization transition and its relevance for Klein-Gordon lattices

We extend earlier work [Phys.Rev.Lett. 84, 3740 (2000)] on the statistical mechanics of the cubic one-dimensional discrete nonlinear Schrodinger (DNLS) equation to a more general class of models, including higher dimensionalities and nonlinearities of arbitrary degree. These extensions are physically motivated by the desire to describe situations with an excitation threshold for creation of localized excitations, as well as by recent work suggesting non-cubic DNLS models to describe Bose-Einstein condensates in deep optical lattices, taking into account the effective condensate dimensionality. Considering ensembles of initial conditions with given values of the two conserved quantities, norm and Hamiltonian, we calculate analytically the boundary of the 'normal' Gibbsian regime corresponding to infinite temperature, and perform numerical simulations to illuminate the nature of the localization dynamics outside this regime for various cases. Furthermore, we show quantitatively how this DNLS localization transition manifests itself for small-amplitude oscillations in generic Klein-Gordon lattices of weakly coupled anharmonic oscillators (in which energy is the only conserved quantity), and determine conditions for existence of persistent energy localization over large time scales.Comment: to be published in Physical Review

Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators

Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allowed to be nonpositive definite according to a real parameter. In this paper, we provide a range of parameter values to ensure the existence of solitary (standing) waves, obtained as Mountain Pass critical points for the associated energy functionals in two different settings, by considering two different classes of potentials: constant potentials and continuous, bounded from below, and coercive potentials.Comment: 26 pages, 2 figure

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for the equation