Ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation

DOI10.1016/J.NA.2020.111831zbMath1436.35118OpenAlexW3010054201MaRDI QIDQ1988440

Xiao-Ping Wang, Fang-Fang Liao

Publication date: 23 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.na.2020.111831

zbMATH Keywords

ground state solutionChoquard equationPohožaev manifoldlocal nonlinear perturbationlower critical exponent

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62)

Related Items (7)

Existence and concentration of solutions for Choquard equations with steep potential Well and doubly critical exponents ⋮ Nehari-type ground state solutions for a Choquard equation with doubly critical exponents ⋮ Multiplicity of concentrating solutions for Choquard equation with critical growth ⋮ Unnamed Item ⋮ Positive ground state solutions for Choquard equations with lower critical exponent and steep well potential ⋮ Semiclassical states for critical Choquard equations ⋮ On the planar axially symmetric Schrödinger-Poisson systems with Choquard nonlinearity

Cites Work

• Unnamed Item
• A guide to the Choquard equation
• On a periodic Schrödinger equation with nonlocal superlinear part
• On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
• Existence of semiclassical ground state solutions for a generalized Choquard equation
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Ground state solutions of Pohožaev type and Nehari type for a class of nonlinear Choquard equations
• Odd symmetry of least energy nodal solutions for the Choquard equation
• Existence and qualitative properties of solutions for Choquard equations with a local term
• Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent
• Minimax theorems
• Infinitely many bound state solutions of Choquard equations with potentials
• Superlinear Schrödinger-Kirchhoff type problems involving the fractional \(p\)-Laplacian and critical exponent
• Critical growth elliptic problems involving Hardy-Littlewood-Sobolev critical exponent in non-contractible domains
• Existence of a ground state solution for Choquard equation with the upper critical exponent
• Semiclassical ground state solutions for critical Schrödinger-Poisson systems with lower perturbations
• Ground state solutions for general Choquard equations with a variable potential and a local nonlinearity
• Ground state solutions of Nehari-Pankov type for Schrödinger equations with local super-quadratic conditions
• Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems
• Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
• Berestycki-Lions conditions on ground state solutions for a nonlinear Schrödinger equation with variable potentials
• On the planar Schrödinger-Poisson system with the axially symmetric potential
• Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials
• A multiplicity result for asymptotically linear Kirchhoff equations
• A fractional Kirchhoff problem involving a singular term and a critical nonlinearity
• Limit profiles and uniqueness of ground states to the nonlinear Choquard equations
• Choquard-type equations with Hardy-Littlewood-Sobolev upper-critical growth
• Multi-bump solutions for Choquard equation with deepening potential well
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Combined effects for fractional Schrödinger–Kirchhoff systems with critical nonlinearities
• Spherically-symmetric solutions of the Schrödinger-Newton equations
• Existence of groundstates for a class of nonlinear Choquard equations
• A critical fractional Choquard–Kirchhoff problem with magnetic field

This page was built for publication: Ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation