Berestycki-Lions conditions on ground state solutions for Kirchhoff-type problems with variable potentials

DOI10.1063/1.5128177zbMath1432.35192arXiv1901.03187OpenAlexW2909570013WikidataQ126541539 ScholiaQ126541539MaRDI QIDQ5218756

Sitong Chen, Xian Hua Tang

Publication date: 5 March 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03187

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (12)

Existence of ground state solutions for Kirchhoff-type problem with variable potential ⋮ Radial and nonradial solutions for nonautonomous Kirchhoff problems ⋮ Ground state solutions of Pohožaev type for Kirchhoff‐type problems with general convolution nonlinearity and variable potential ⋮ Ground state solutions for planar periodic Kirchhoff type equation with critical exponential growth ⋮ Multiple solutions for fractional Kirchhoff equation with critical or supercritical nonlinearity ⋮ Improved results on planar Kirchhoff-type elliptic problems with critical exponential growth ⋮ Existence, multiplicity and nonexistence results for Kirchhoff type equations ⋮ Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent ⋮ Existence of ground states for Kirchhoff-type problems with general potentials ⋮ Ground state solutions for Kirchhoff-type problems with convolution nonlinearity and Berestycki-Lions type conditions ⋮ A class of Kirchhoff-type problems involving the concave-convex nonlinearities and steep potential Well ⋮ Existence of positive solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)

Cites Work

• An autonomous Kirchhoff-type equation with general nonlinearity in \(\mathbb{R}^N\)
• Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents
• The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity.
• Existence and multiplicity of solutions for Kirchhoff type equations
• The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in \(\mathbb{R}^3\)
• Nonlinear scalar field equations. I: Existence of a ground state
• Nontrivial solutions of Kirchhoff-type problems via the Yang index
• Minimax theorems
• Multiple solutions for the nonhomogeneous Kirchhoff equation on \(\mathbb R^N\)
• Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument
• Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent
• Semiclassical ground state solutions for critical Schrödinger-Poisson systems with lower perturbations
• Ground state solutions of Nehari-Pankov type for Schrödinger equations with local super-quadratic conditions
• 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 states for Kirchhoff equations without compact condition
• Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials
• Existence and asymptotic behavior of vector solutions for coupled nonlinear Kirchhoff-type systems
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• The critical problem of Kirchhoff type elliptic equations in dimension four
• Positive solutions for a quasilinear elliptic equation of Kirchhoff type
• The Schrödinger-Poisson equation under the effect of a nonlinear local term
• Infinitely many positive solutions for Kirchhoff-type problems
• Concentrating Bound States for Kirchhoff Type Problems in ℝ³ Involving Critical Sobolev Exponents
• 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
• A Note on a Mountain Pass Characterization of Least Energy Solutions
• Infinitely many solutions for fractional Kirchhoff-Schrödinger-Poisson systems
• Nonlinear Analysis - Theory and Methods
• A positive solution for a nonlinear Schroedinger equation on R^N
• A note on the elliptic Kirchhoff equation in ℝ^Nperturbed by a local nonlinearity

This page was built for publication: Berestycki-Lions conditions on ground state solutions for Kirchhoff-type problems with variable potentials