Ground states and non-existence results for Choquard type equations with lower critical exponent and indefinite potentials

DOI10.1016/j.na.2020.111863zbMath1440.35144OpenAlexW3013988341MaRDI QIDQ2183465

Qingfang Wu, Jing Chen, Dongdong Qin

Publication date: 27 May 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.2020.111863

zbMATH Keywords

existence of solutionscritical exponentPohožaev identityChoquard-type equations

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items

Ground state solutions and infinitely many solutions for a nonlinear Choquard equation ⋮ Existence of ground state solutions for a class of Choquard equations with local nonlinear perturbation and variable potential ⋮ Existence of ground state solutions for critical fractional Choquard equations involving periodic magnetic field ⋮ Existence of positive solution for the Choquard equation in exterior domain ⋮ Strongly indefinite Choquard equation in ℝ2 with critical exponential growth ⋮ The ground state solutions to discrete nonlinear Choquard equations with Hardy weights ⋮ Ground state solution for fractional \(p\)-Choquard equations with upper critical exponent ⋮ Saddle solutions for the critical Choquard equation ⋮ Ground states and multiple solutions for Choquard-Pekar equations with indefinite potential and general nonlinearity ⋮ Existence and asymptotic behavior of ground states for Choquard-Pekar equations with Hardy potential and critical reaction

Cites Work

• Unnamed Item
• Pointwise bounds and blow-up for Choquard-Pekar inequalities at an isolated singularity
• Nodal solutions for the Choquard equation
• Multiple solutions to a magnetic nonlinear Choquard equation
• Solutions of Schrödinger equations with inverse square potential and critical nonlinearity
• Semi-classical states for the Choquard equation
• A guide to the Choquard equation
• Choquard equations under confining external potentials
• Ground state solutions for Hamiltonian elliptic system with inverse square potential
• On a periodic Schrödinger equation with nonlocal superlinear part
• On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
• Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations
• Classification of positive solitary solutions of the nonlinear Choquard equation
• On a class of nonlinear Schrödinger equations
• On fractional Schrödinger equation with periodic and asymptotically periodic conditions
• Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent
• Solutions of Hartree-Fock equations for Coulomb systems
• Minimax theorems
• Positive and sign changing solutions to a nonlinear Choquard equation
• Dual variational methods in critical point theory and applications
• Semiclassical solutions for Choquard equations with Berestycki-Lions type conditions
• Standing waves with a critical frequency for nonlinear Choquard equations
• Saddle solutions for the Choquard equation
• Nonlocal perturbations of the fractional Choquard equation
• Limit profiles and uniqueness of ground states to the nonlinear Choquard equations
• Choquard-type equations with Hardy-Littlewood-Sobolev upper-critical growth
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• On a semilinear Schrödinger equation with critical Sobolev exponent
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• The existence of a nontrivial solution to a nonlinear elliptic problem of linking type without the Ambrosetti-Rabinowitz condition
• Strongly interacting bumps for the Schrödinger–Newton equations
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Nonlinear Analysis - Theory and Methods
• Spherically-symmetric solutions of the Schrödinger-Newton equations
• The Schrödinger–Newton equation as a non-relativistic limit of self-gravitating Klein–Gordon and Dirac fields
• Existence of groundstates for a class of nonlinear Choquard equations
• A critical fractional Choquard–Kirchhoff problem with magnetic field