Existence and asymptotic behavior of standing wave solutions for a class of generalized quasilinear Schrödinger equations with critical Sobolev exponents

DOI10.3233/ASY-191586zbMath1472.35350OpenAlexW2985453052MaRDI QIDQ4999965

Dongdong Qin, Xianjiu Huang, Bitao Cheng, Jian-Hua Chen

Publication date: 5 July 2021

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/asy-191586

zbMATH Keywords

existenceasymptotic behaviorcritical exponentsground state solutionsgeneralized quasilinear Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (4)

Some existence results on a class of generalized quasilinear Schrödinger equations with Choquard type ⋮ On concentration of solutions for quasilinear Schrödinger equations with critical growth in the plane ⋮ Existence and concentration behavior of ground states for a generalized quasilinear Choquard equation involving steep potential well ⋮ Existence and asymptotic behaviour for the \(2D\)-generalized quasilinear Schrödinger equations involving Trudinger-Moser nonlinearity and potentials

Cites Work

• Multiple solutions to a class of generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation
• Bound states to critical quasilinear Schrödinger equations
• Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth
• Existence and concentration of ground state solutions for a subcubic quasilinear problem via Pohozaev manifold
• Two types of quasilinear elliptic equations with degenerate coerciveness and slightly superlinear growth
• Concentrating soliton solutions for quasilinear Schrödinger equations involving critical Sobolev exponents
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• Soliton solutions for quasilinear Schrödinger equations with critical growth
• Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in \(\mathbb R^N\)
• Ground state solutions of scalar field fractional Schrödinger equations
• Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations
• Existence and concentration of solitary waves for a class of quasilinear Schrödinger equations
• Solitary waves for a class of quasilinear Schrödinger equations in dimension two
• On instability of excited states of the nonlinear Schrödinger equation
• On a class of nonlinear Schrödinger equations
• Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
• Global existence of small solutions to a relativistic nonlinear Schrödinger equation
• On the existence of soliton solutions to quasilinear Schrödinger equations
• Ground state sign-changing solutions for a class of generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation
• Infinite dimensional Morse theory and multiple solution problems
• Some existence results for superlinear elliptic boundary value problems involving critical exponents
• On the variational principle
• Soliton solutions for quasilinear Schrödinger equations. II.
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• Soliton solutions for generalized quasilinear Schrödinger equations
• Bound state solutions of sublinear Schrödinger equations with lack of compactness
• Existence and concentration behavior of positive solutions for a quasilinear Schrödinger equation
• The concentration behavior of ground state solutions for a fractional Schrödinger-Poisson system
• Non-Nehari manifold method for a class of generalized quasilinear Schrödinger equations
• Solutions of perturbed Schrödinger equations with critical nonlinearity
• Standing waves for a class of quasilinear Schrödinger equations
• Existence of ground state solutions to a generalized quasilinear Schrödinger-Maxwell system
• Concentrating Bound States for Kirchhoff Type Problems in ℝ³ Involving Critical Sobolev Exponents
• Existence of solution for a generalized quasilinear elliptic problem
• Multiple solutions for generalized quasilinear Schrödinger equations
• Ground state solutions and geometrically distinct solutions for generalized quasilinear Schrödinger equation
• Existence, multiplicity, and concentration of solutions for generalized quasilinear Schrödinger equations with critical growth
• Solutions for Quasilinear Schrödinger Equations via the Nehari Method
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Evolution theorem for a class of perturbed envelope soliton solutions
• Some properties of weak solutions of nonlinear scalar field equations
• Existence of ground states for a modified nonlinear Schrödinger equation
• Nash moser methods for the solution of quasilinear schrödinger equations
• Existence and nonexistence of positive solutions for a class of generalized quasilinear Schrödinger equations involving a Kirchhoff-type perturbation with critical Sobolev exponent
• Combined effects for fractional Schrödinger–Kirchhoff systems with critical nonlinearities
• Soliton solutions for quasilinear Schrödinger equations, I
• Nodal soliton solutions for generalized quasilinear Schrödinger equations
• Nodal soliton solutions for quasilinear Schrödinger equations with critical exponent
• Existence and concentration of positive solutions for quasilinear Schrödinger equations with critical growth
• Ground states for fractional Schrödinger equations with critical growth
• Existence of nodal solutions of nonlinear elliptic equations
• Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials

This page was built for publication: Existence and asymptotic behavior of standing wave solutions for a class of generalized quasilinear Schrödinger equations with critical Sobolev exponents