Infinitely many positive solutions for a Schrödinger-Poisson system

DOI10.1016/j.na.2011.05.057zbMath1225.35226arXiv1001.5363OpenAlexW2011519342MaRDI QIDQ5892643

Pietro D'Avenia, Alessio Pomponio, Giusi Vaira

Publication date: 22 July 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.5363

zbMATH Keywords

perturbation methodnon-autonomous Schrödinger-Poisson system

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items

Existence of ground state solutions for the Schrödinger-Poisson systems, On a Schrödinger-Poisson system with singularity and critical nonlinearities, Solutions of a Schrödinger-Poisson system with combined nonlinearities, A positive solution of a Schrödinger-Poisson system with critical exponent, Ground state sign-changing solutions for a Schrödinger-Poisson system with a critical nonlinearity in \(\mathbb{R}^3\), Infinitely many solutions for Schrödinger–Newton equations, On the Schrödinger-Poisson system with a general indefinite nonlinearity, Multiple solutions for the fractional Schrödinger–Poisson system with concave–convex nonlinearities, Existence of multiple positive solutions for Schrödinger-Poisson systems with critical growth, Non-degeneracy of multi-peak solutions for the Schrödinger-Poisson problem, Ground state solutions for Schrödinger–Poisson systems on ℝ3$$ {\mathbb{R}}^3 $$ with a weighted critical exponent, Monotonic sequences of minimal solutions for semipositone elliptic systems, On the Schrödinger-Maxwell system involving sublinear terms, Existence and asymptotic behavior of bound states for a class of nonautonomous Schrödinger-Poisson system, Multiple positive solutions for a Schrödinger-Newton system with sign-changing potential, An asymptotically linear Schrödinger-Poisson system on \(\mathbb R^3\), Two positive solutions of a class of Schrödinger-Poisson system with indefinite nonlinearity, Multiple positive solutions of a class of non autonomous Schrödinger-Poisson systems, Infinitely many solutions for a Schrödinger-Poisson system with concave and convex nonlinearities, Solitons in Schrödinger-Maxwell equations, INFINITELY MANY BOUND STATE SOLUTIONS OF SCHRÖDINGER-POISSON EQUATIONS IN R³, Connected sets of positive solutions of elliptic systems in exterior domains, Ground state and nodal solutions for a Schrödinger-Poisson equation with critical growth, Ground state solutions for Schrödinger-Poisson systems with multiple weighted critical exponents, Positive and sign-changing solutions of a Schrödinger-Poisson system involving a critical nonlinearity, Ground state sign-changing solutions for a Schrödinger-Poisson system with a 3-linear growth nonlinearity, On ground state solutions for the Schrödinger-Poisson equations with critical growth, Positive solutions for a Schrödinger-Poisson system with singularity and critical exponent, Existence of multi-bump solutions for the Schrödinger-Poisson system, Existence and multiplicity of solutions for Schrödinger-Poisson equations with sign-changing potential

Cites Work

• Unnamed Item
• Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential
• Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem
• On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations
• Ground state solutions for the nonlinear Schrödinger-Maxwell equations
• On the existence of solutions for the Schrödinger-Poisson equations
• On the Schrödinger-Maxwell equations under the effect of a general nonlinear term
• Infinitely many solutions for the prescribed scalar curvature problem on \(\mathbb S^N\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• An eigenvalue problem for the Schrödinger-Maxwell equations
• Concentration and compactness in nonlinear Schrödinger-Poisson system with a general nonlinearity
• Infinitely many positive solutions for the nonlinear Schrödinger equations in \(\mathbb R^N\)
• Positive solution for a nonlinear stationary Schrödinger-Poisson system in \(\mathbb R^3\)
• The Schrödinger-Poisson equation under the effect of a nonlinear local term
• Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations
• Positive solutions for some non-autonomous Schrödinger-Poisson systems
• INFINITELY MANY POSITIVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER–POISSON SYSTEM
• On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials
• Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations
• A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture
• Existence and Stability of Standing Waves For Schrödinger-Poisson-Slater Equation
• Infinitely many positive solutions for a Schrödinger-Poisson system
• On interacting bumps of semi-classical states of nonlinear Schrödinger equations.