Groundstates for Choquard type equations with Hardy–Littlewood–Sobolev lower critical exponent

DOI10.1017/prm.2018.135zbMath1437.35329arXiv1709.09448OpenAlexW2756522253MaRDI QIDQ4961014

Jean Van Schaftingen, Daniele Cassani, Jian Jun Zhang

Publication date: 24 April 2020

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.09448

zbMATH Keywords

ground statesexistence and nonexistenceChoquard equation

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations (35J61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (28)

Existence of ground state solutions for a class of Choquard equations with local nonlinear perturbation and variable potential ⋮ Ground states for Schrödinger-Kirchhoff equations of fractional \(p\)-Laplacian involving logarithmic and critical nonlinearity ⋮ Quasilinear logarithmic Choquard equations with exponential growth in \(\mathbb{R}^N\) ⋮ Infinitely many non-radial positive solutions for Choquard equations ⋮ Infinitely many solutions for the Brézis-Nirenberg problem with nonlinear Choquard equations ⋮ Existence of ground state solutions for critical fractional Choquard equations involving periodic magnetic field ⋮ Existence and concentration of solutions for Choquard equations with steep potential Well and doubly critical exponents ⋮ Sign-changing solutions to the critical Choquard equation ⋮ Supersolutions to nonautonomous Choquard equations in general domains ⋮ Bifurcation into spectral gaps for strongly indefinite Choquard equations ⋮ Existence and stability of standing waves for the Choquard equation with partial confinement ⋮ Classification and qualitative analysis of positive solutions of the nonlinear Hartree type system ⋮ Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case ⋮ Multiple solutions of \(p\)-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents ⋮ Semi-classical states for the Choquard equations with doubly critical exponents: Existence, multiplicity and concentration ⋮ Semiclassical states to the nonlinear Choquard equation with critical growth ⋮ Ground state solution for fractional \(p\)-Choquard equations with upper critical exponent ⋮ Unnamed Item ⋮ Positive ground state solutions for Choquard equations with lower critical exponent and steep well potential ⋮ Groundstates for Choquard type equations with weighted potentials and Hardy-Littlewood-Sobolev lower critical exponent ⋮ Localized nodal solutions for semiclassical Choquard equations ⋮ Saddle solutions for the critical Choquard equation ⋮ Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent ⋮ Semiclassical states for critical Choquard equations ⋮ Existence and asymptotical behavior of the minimizer of Hartree type equation with periodic potentials ⋮ Schrödinger-Newton equations in dimension two via a Pohozaev-Trudinger log-weighted inequality ⋮ Existence of solutions for critical Choquard equations via the concentration-compactness method ⋮ Ground states of coupled critical Choquard equations with weighted potentials

Cites Work

• Groundstates and radial solutions to nonlinear Schrödinger-Poisson-Slater equations at the critical frequency
• A guide to the Choquard equation
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• On gravity's role in quantum state reduction
• Choquard-type equations with Hardy-Littlewood-Sobolev upper-critical growth
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Schrödinger semigroups
• Asymptotics for the polaron
• Mean field dynamics of boson stars
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
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