Semiclassical ground state solutions for critical Schrödinger-Poisson systems with lower perturbations

DOI10.1016/j.jde.2019.09.041zbMath1436.35078OpenAlexW2976400486MaRDI QIDQ2288030

Alessio Fiscella, Sitong Chen, Patrizia Pucci, Xian Hua Tang

Publication date: 16 January 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2019.09.041

zbMATH Keywords

critical growthSchrödinger-Poisson systemconcentrationsemiclassical state

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Second-order elliptic systems (35J47)

Related Items (54)

Existence and concentration of solution for Schrödinger-Poisson system with local potential ⋮ Singularly perturbed quasilinear Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions ⋮ Schrödinger–Poisson system with zero mass and convolution nonlinearity in R 2 ⋮ Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations ⋮ Nehari type ground state solutions for periodic Schrödinger–Poisson systems with variable growth ⋮ Existence and concentration of ground-states for fractional Choquard equation with indefinite potential ⋮ Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group ⋮ Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system ⋮ Axially symmetric solutions of the Schrödinger-Poisson system with zero mass potential in \(\mathbb{R}^2\) ⋮ Semiclassical states for singularly perturbed Schrödinger-Poisson systems with a general Berestycki-Lions or critical nonlinearity ⋮ Nehari-type ground state solutions for a Choquard equation with doubly critical exponents ⋮ The existence of ground state solutions for a Schrödinger-Bopp-Podolsky system with convolution nonlinearity ⋮ Positive solutions for the Schrödinger–Poisson system with steep potential well ⋮ Groundstates of the Schrödinger-Poisson-Slater equation with critical growth ⋮ On the critical Kirchhoff problems with super-linear nonlinearities and variable potentials ⋮ Semiclassical solutions for a critical Choquard-Poisson system with competitive potentials ⋮ Existence and nonexistence of ground state solutions for a Schrödinger–Poisson–Slater equation ⋮ Ground‐state solution of a nonlinear fractional Schrödinger–Poisson system ⋮ Solutions of a quasilinear Schrödinger-Poisson system with linearly bounded nonlinearities ⋮ Existence of ground state solutions for a Choquard double phase problem ⋮ Existence and concentration behavior of positive solutions to Schrödinger-Poisson-Slater equations ⋮ On the nonlocal Schrödinger‐poisson type system in the Heisenberg group ⋮ On the planar Schrödinger–Poisson system with zero mass potential ⋮ Existence of solutions for a Schrödinger-Poisson system with critical nonlocal term and general nonlinearity ⋮ Axially symmetric solutions for the planar Schrödinger-Poisson system with critical exponential growth ⋮ Normalized solutions for Choquard equations with general nonlinearities ⋮ Nontrivial solution for Klein-Gordon equation coupled with Born-Infeld theory with critical growth ⋮ Ground state solutions to a class of critical Schrödinger problem ⋮ Existence of multi-bump solutions for the magnetic Schrödinger-Poisson system in \(\mathbb{R}^3\) ⋮ On critical Klein-Gordon-Maxwell systems with super-linear nonlinearities ⋮ Nodal solutions for the Schrödinger-Poisson equations with convolution terms ⋮ Ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation ⋮ The existence of least energy sign-changing solution for Kirchhoff-type problem with potential vanishing at infinity ⋮ Some results of nontrivial solutions for Klein-Gordon-Maxwell systems with local super-quadratic conditions ⋮ On the planar Schrödinger-Poisson system with zero mass and critical exponential growth ⋮ Concentration phenomena at saddle points of potential for Schrödinger-Poisson systems ⋮ Existence and multiplicity of solutions for Dirichlet problem of \(p(x)\)-Laplacian type without the Ambrosetti-Rabinowitz condition ⋮ Ground state solutions for general Choquard equations with a variable potential and a local nonlinearity ⋮ Normalized solutions of nonautonomous Kirchhoff equations: sub- and super-critical cases ⋮ Existence of ground states for Kirchhoff-type problems with general potentials ⋮ Nontrivial solutions for the Choquard equation with indefinite linear part and upper critical exponent ⋮ Berestycki-Lions conditions on ground state solutions for Kirchhoff-type problems with variable potentials ⋮ Positive, negative, and sign-changing solutions to a quasilinear Schrödinger equation with a parameter ⋮ Nontrivial solutions for a nonlinear Schrödinger equation with nonsymmetric coefficients ⋮ Existence criteria of ground state solutions for Schrödinger-Poisson systems with a vanishing potential ⋮ Ground state solutions of the non-autonomous Schrödinger-Bopp-Podolsky system ⋮ New insights on weighted pseudo almost periodic solutions in a Lasota-Wazewska system ⋮ High and low perturbations of Choquard equations with critical reaction and variable growth ⋮ Asymptotic profile of ground states for the Schrödinger-Poisson-Slater equation ⋮ Ground states for reaction-diffusion equations with spectrum point zero ⋮ Ground state solutions for the nonlinear Schrödinger-Bopp-Podolsky system with critical Sobolev exponent ⋮ Ground state solutions of Schrödinger–Poisson systems with asymptotically constant potential ⋮ The multiplicity of solutions for the critical Schrödinger–Poisson system with competing potentials ⋮ Positive solutions for a nonhomogeneous Schrödinger-Poisson system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and concentration of positive solutions for semilinear Schrödinger-Poisson systems in \({\mathbb{R}^{3}}\)
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Nonlinear scalar field equations. I: Existence of a ground state
• Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem
• Ground state solutions for some Schrödinger-Poisson systems with periodic potentials
• Ground state solutions for the nonlinear Schrödinger-Maxwell equations
• On the existence of solutions for the Schrödinger-Poisson equations
• Positive solutions for Schrödinger-Poisson equations with a critical exponent
• The Thomas-Fermi-von Weizsäcker theory of atoms and molecules
• On a class of nonlinear Schrödinger equations
• An eigenvalue problem for the Schrödinger-Maxwell equations
• Solutions of Hartree-Fock equations for Coulomb systems
• Minimax theorems
• Multiplicity and concentration of positive solutions for the Schrödinger-Poisson equations
• Concentration and compactness in nonlinear Schrödinger-Poisson system with a general nonlinearity
• Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials
• Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials
• The Schrödinger-Poisson equation under the effect of a nonlinear local term
• Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth
• Standing waves for nonlinear Schrödinger equations involving critical growth
• Schrödinger semigroups
• The existence of a nontrivial solution to a nonlinear elliptic problem of linking type without the Ambrosetti-Rabinowitz condition
• Existence of solutions with prescribed norm for semilinear elliptic equations
• On decay of solutions to nonlinear Schrödinger equations
• MULTIPLE BOUND STATES FOR THE SCHRÖDINGER–POISSON PROBLEM
• On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials
• Thomas-fermi and related theories of atoms and molecules
• A ecessary and Sufficient Condition for The Stability of General molecular Systems
• Bounded Palais-Smale mountain-pass sequences
• Nonlinear Analysis - Theory and Methods
• Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations
• SEMICLASSICAL STATES FOR COUPLED SCHRÖDINGER–MAXWELL EQUATIONS: CONCENTRATION AROUND A SPHERE
• Multiple semiclassical states for coupled Schrödinger-Poisson equations with critical exponential growth
• The existence and concentration of positive solutions for a nonlinear Schrödinger-Poisson system with critical growth
• On Bound States Concentrating on Spheres for the Maxwell--Schrödinger Equation

This page was built for publication: Semiclassical ground state solutions for critical Schrödinger-Poisson systems with lower perturbations