Ground states for nonlinear Kirchhoff equations with critical growth

DOI10.1007/s10231-012-0286-6zbMath1300.35016OpenAlexW2062916296MaRDI QIDQ2015001

Wen Ming Zou, Xiao-Ming He

Publication date: 18 June 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-012-0286-6

zbMATH Keywords

positive solutionsvariational methodspotential functionlack of compactnessLjusternik-Schnirelmann categoryKirchhoff type equation with critical growth

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Variational methods for second-order elliptic equations (35J20) Integro-partial differential equations (35R09)

Related Items

Bounded state solutions of Kirchhoff type problems with a critical exponent in high dimension, Exact Number of Positive Solutions for the Kirchhoff Equation, A nonhomogeneous fractional \(p\)-Kirchhoff type problem involving critical exponent in \(\mathbb{R}^N\), Bound state solutions of Kirchhoff type problems with critical exponent, Existence and multiplicity of solutions for generalized asymptotically linear Schrödinger-Kirchhoff equations, Singular perturbed Kirchhoff type problem with critical exponent, Ground states for Schrödinger-Kirchhoff equations of fractional \(p\)-Laplacian involving logarithmic and critical nonlinearity, Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth, Multiplicity of solutions for Kirchhoff type equations involving critical Sobolev exponents in high dimension, Ground states for Kirchhoff-type equations with critical growth, Sign-changing solutions for Kirchhoff-type problems involving variable-order fractional Laplacian and critical exponents, Existence and concentration of ground state solutions for critical Kirchhoff-type equation with steep potential well, Multiple positive solutions to a Kirchhoff type problem involving a critical nonlinearity in \(\mathbb{R}^3\), A multiplicity result for asymptotically linear Kirchhoff equations, Existence and convergence of the least energy sign-changing solutions for nonlinear Kirchhoff equations on locally finite graphs, Solutions of a Schrödinger-Kirchhoff-Poisson system with concave-convex nonlinearities, Infinitely many small solutions for the Kirchhoff equation with local sublinear nonlinearities, Nodal solution for critical Kirchhoff-type equation with fast increasing weight in \(\mathbb{R}^2\), Existence and multiple solutions for the critical fractional p‐Kirchhoff type problems involving sign‐changing weight functions, Existence and multiplicity of solutions for asymptotically linear Schrödinger-Kirchhoff equations, Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities, Nodal solutions to ( p , q )-Laplacian equations with critical growth, Infinitely many bound state solutions of Kirchhoff problem in \(\mathbb R^3\), The third solution for a Kirchhoff-type problem with a critical exponent, High energy positive solutions for a coupled Kirchhoff system, Least energy sign-changing solution for \(N\)-Kirchhoff problems with logarithmic and exponential nonlinearities, Infinitely many localized semiclassical states for nonlinear Kirchhoff-type equation, Least-energy nodal solutions of critical Kirchhoff problems with logarithmic nonlinearity, Nodal solutions for a Kirchhoff type problem in \(\mathbb{R}^N\), Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in \(\mathbb R^N\), A critical fractional \(p\)-Kirchhoff type problem involving discontinuous nonlinearity, Existence and concentration of positive solutions for Kirchhoff-type problems with a steep well potential, Normalized solutions for the Kirchhoff equation on noncompact metric graphs ^*, Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions, Ground state solutions to a class of critical Schrödinger problem, The existence and nonexistence results of ground state nodal solutions for a Kirchhoff type problem, Existence of sign-changing solutions for a class ofp-Laplacian Kirchhoff-type equations, Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation, Multiplicity of positive solutions for a class of critical Sobolev exponent problems involving Kirchhoff-type nonlocal term, Superlinear Schrödinger-Kirchhoff type problems involving the fractional \(p\)-Laplacian and critical exponent, Existence of positive solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^n\), Classification results for Kirchhoff equations in RN, Multiple positive solutions to a Kirchhoff type problem involving a critical nonlinearity, Existence and multiplicity of solutions for a superlinear Kirchhoff-type equations with critical Sobolev exponent in \(\mathbb R^N\), On bi-nonlocal problem for elliptic equations with Neumann boundary conditions, Existence and concentration of solutions for a class of elliptic Kirchhoff-Schrödinger equations with subcritical and critical growth, A study on the critical Kirchhoff problem in high-dimensional space, Least energy sign-changing solutions of Kirchhoff-type equation with critical growth, Infinitely many sign-changing solutions for Kirchhoff type equations, Existence and concentration of ground state solutions for a class of Kirchhoff-type problems, Semi-classical solutions for Kirchhoff type problem with a critical frequency, Bounded state solution of degenerate Kirchhoff type problem with a critical exponent, Nodal solutions for Kirchhoff equations with Choquard nonlinearity, Normalized solutions of Kirchhoff equations with critical and subcritical nonlinearities: the defocusing case, Positive solutions for Kirchhoff-type equations with critical exponent in \(\mathbb{R}^N\), Existence and multiplicity of nontrivial solutions for \(p\)-Laplacian Schrödinger-Kirchhoff-type equations

Cites Work

• Unnamed Item
• Unnamed Item
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Nontrivial solutions of Kirchhoff-type problems via the Yang index
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Multiplicity of solutions for a class of Kirchhoff type problems
• Regularity for a more general class of quasilinear equations
• On a class of nonlinear Schrödinger equations
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
• Semiclassical states of nonlinear Schrödinger equations
• Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations
• Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
• Positive solutions for a nonlinear nonlocal elliptic transmission problem
• Multiple positive solutions for a nonlinear Schrödinger equation
• Multiplicity of solutions for a class of quasilinear problem in exterior domains with Neumann conditions
• On concentration of positive bound states of nonlinear Schrödinger equations
• On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• On the variational principle
• Semi-classical states of nonlinear Schrödinger equations: a variational reduction method
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
• On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in \(\mathbb R^{N}\)
• On the Schrödinger equation involving a critical Sobolev exponent and magnetic field
• Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials
• Infinitely many positive solutions for Kirchhoff-type problems
• Standing waves for nonlinear Schrödinger equations with a general nonlinearity
• Solutions of perturbed Schrödinger equations with critical nonlinearity
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• On a class of nonlocal elliptic problems with critical growth
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• On the Well-Posedness of the Kirchhoff String
• On harnack type inequalities and their application to quasilinear elliptic equations
• Multiplicity results for some nonlinear Schrödinger equations with potentials
• Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation