Choquard equations with critical nonlinearities

DOI10.1142/S0219199719500238zbMath1440.35139arXiv1808.05814MaRDI QIDQ5113114

Shiwang Ma, Xinfu Li

Publication date: 10 June 2020

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.05814

zbMATH Keywords

critical exponentsChoquard equationPohožaev identityexistence of ground state solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items (37)

Nonexistence, existence and symmetry of normalized ground states to Choquard equations with a local perturbation ⋮ Existence of groundstates for Choquard type equations with Hardy-Littlewood-Sobolev critical exponent ⋮ Existence and concentration of ground state solutions for critical Kirchhoff-type equation involving Hartree-type nonlinearities ⋮ Infinitely many solutions for the Brézis-Nirenberg problem with nonlinear Choquard equations ⋮ Normalized ground states for the critical fractional Choquard equation with a local perturbation ⋮ Semiclassical states for Schrödinger-Poisson system with Hartree-type nonlinearity ⋮ Ground state solutions for Choquard equations with Hardy potentials and critical nonlinearity ⋮ Normalized Solutions for Lower Critical Choquard Equations with Critical Sobolev Perturbation ⋮ Multiple and asymptotical behavior of solutions to a Choquard equation with singularity ⋮ Normalized solutions for the fractional Choquard equations with Hardy-Littlewood-Sobolev upper critical exponent ⋮ Normalized solutions to the critical Choquard-type equations with weakly attractive potential and nonlocal perturbation ⋮ Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation ⋮ Prescribed mass standing waves for energy critical Hartree equations ⋮ Asymptotic properties of ground states to the Choquard equation with generalized autonomous perturbation ⋮ Semiclassical solutions for a critical Choquard-Poisson system with competitive potentials ⋮ Normalized solutions for the critical Schrödinger-Bopp-Podolsky system ⋮ Normalized solutions for the Schrödinger-Poisson system with doubly critical growth ⋮ On critical double phase Choquard problems with singular nonlinearity ⋮ Normalized ground states for the fractional Schrödinger-Poisson system with critical nonlinearities ⋮ The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation ⋮ Normalized solutions to nonlinear scalar field equations with doubly nonlocal terms and critical exponent ⋮ Multiplicity and concentration of positive solutions for critical Choquard equations with concave perturbation ⋮ Normalized solutions to lower critical Choquard equation with a local perturbation ⋮ Localized nodal solutions for system of critical Choquard equations ⋮ Asymptotic profiles for a nonlinear Schrödinger equation with critical combined powers nonlinearity ⋮ Unnamed Item ⋮ Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation ⋮ Localized nodal solutions for semiclassical Choquard equations ⋮ Semiclassical states for critical Choquard equations ⋮ Unnamed Item ⋮ Ground state solutions for general Choquard equations with a variable potential and a local nonlinearity ⋮ Existence of normalized ground states for the Sobolev critical Schrödinger equation with combined nonlinearities ⋮ Choquard equations via nonlinear Rayleigh quotient for concave-convex nonlinearities ⋮ High and low perturbations of Choquard equations with critical reaction and variable growth ⋮ The existence of positive solutions to the Choquard equation with critical exponent and logarithmic term ⋮ Standing waves to upper critical Choquard equation with a local perturbation: multiplicity, qualitative properties and stability ⋮ Existence and asymptotic behavior of ground states for Choquard-Pekar equations with Hardy potential and critical reaction

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