Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions

DOI10.1515/anona-2020-0007zbMath1421.35068arXiv1903.10347OpenAlexW2964006947MaRDI QIDQ2311843

Sitong Chen, Xian Hua Tang

Publication date: 4 July 2019

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.10347

zbMATH Keywords

singular perturbationground state solutionChoquard equationBerestycki-Lions assumptionsPohožaev mainfold

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

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Cites Work

• Unnamed Item
• Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
• Existence of a positive solution for nonlinear Schrödinger equations with general nonlinearity
• Semi-classical states for the Choquard equation
• A guide to the Choquard equation
• Infinitely many solutions for the Schrödinger equations in \(\mathbb R^N\) with critical growth
• Existence of semiclassical ground state solutions for a generalized Choquard equation
• Nonlinear scalar field equations. I: Existence of a ground state
• Ground state solutions of scalar field fractional Schrödinger equations
• On a class of nonlinear Schrödinger equations
• Ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth
• Improved results for Klein-Gordon-Maxwell systems with general nonlinearity
• Zero mass case for a fractional Berestycki-Lions-type problem
• Odd symmetry of least energy nodal solutions for the Choquard equation
• Nontrivial solutions for Schrödinger equation with local super-quadratic conditions
• Minimax theorems
• Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
• Singularly perturbed critical Choquard equations
• Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems
• Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity
• Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
• 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
• Entire nonradial solutions for non-cooperative coupled elliptic system with critical exponents in \(\mathbb R^3\)
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities
• Existence of solutions with prescribed norm for semilinear elliptic equations
• Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions
• Strongly interacting bumps for the Schrödinger–Newton equations
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Bounded Palais-Smale mountain-pass sequences
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• Ground state solutions for generalized quasilinear Schrödinger equations with variable potentials and Berestycki-Lions nonlinearities
• A positive solution for a nonlinear Schroedinger equation on R^N
• Spherically-symmetric solutions of the Schrödinger-Newton equations
• A remark on least energy solutions in $\mathbf {R}^N$
• Existence of groundstates for a class of nonlinear Choquard equations
• A critical fractional Choquard–Kirchhoff problem with magnetic field

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