Ground state solutions for quasilinear Schrödinger equations with variable potential and superlinear reaction
type: Item
instance of: scholarly article
title: Ground state solutions for quasilinear Schrödinger equations with variable potential and superlinear reaction
zbMATH Open document ID: 1460.35100
author: Sitong Chen
author: Vicenţiu D. Rădulescu
author: Binlin Zhang
author: X. H. Tang
published in: Revista Matemática Iberoamericana
publication date: 2021-03-07T00:00:00Z
review text: The authors consider a quasilinear Schrödinger equation of the form \[ -\Delta u+V(x)u-\frac{1}{2}\Delta \left(u^2\right)u=g(u),\quad x\in\mathbb{R}^N, \] where \(N \geq 3\), \(V\in C(\mathbb{R}^N,[0,\infty))\) and \(g\in C(\mathbb{R},\mathbb{R})\) is superlinear at infinity. Under very general assumptions on \(V\) and \(g\) and by using variational tools and some new analytic techniques, it is shown that the problem above admits a ground state solution, where a solution is called a ground state solution if its energy is minimal among all nontrivial solutions.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 7318493
zbMATH Keywords: quasilinear Schrödinger equation
zbMATH Keywords: ground state solution
zbMATH Keywords: Pohozaev identity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/1175
OpenAlex ID: W3006228464
cites work: Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials
cites work: Existence of ground state solutions for quasilinear Schrödinger equations with super-quadratic condition
cites work: Existence and asymptotic behavior of sign-changing solutions for fractional Kirchhoff-type problems in low dimensions
cites work: Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity
cites work: Solutions for a quasilinear Schrödinger equation: a dual approach.
cites work: Ground state solutions for generalized quasilinear Schrödinger equations without \((AR)\) condition
cites work: Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations
cites work: On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
cites work: Evolution theorem for a class of perturbed envelope soliton solutions
cites work: Soliton solutions for quasilinear Schrödinger equations. II.
cites work: Solutions for Quasilinear Schrödinger Equations via the Nehari Method
cites work: On the local well posedness of quasilinear Schrödinger equations in arbitrary space dimension
cites work: On the existence of soliton solutions to quasilinear Schrödinger equations
cites work: Existence of ground states for a modified nonlinear Schrödinger equation
cites work: Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials
cites work: Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
cites work: Ground state solutions of Nehari-Pankov type for Schrödinger equations with local super-quadratic conditions
cites work: Ground state sign-changing solutions for the Schrödinger-Kirchhoff equation in \(\mathbb{R}^3\)
cites work: Minimax theorems
cites work: Radial solutions for quasilinear Schrödinger equations without 4-superlinear condition
cites work: Existence of a bound state solution for quasilinear Schrödinger equations
cites work: Existence of solutions for a quasilinear Schrödinger equation with subcritical nonlinearities
cites work: Ground state solutions for a quasilinear Schrödinger equation
cites work: Existence of infinitely many solutions for a quasilinear elliptic equation
DOI: 10.4171/RMI/1175
description: scientific article; zbMATH DE number 7318493