Existence of solution to \(p\)-Kirchhoff type problem in \(\mathbb R^N\) via Nehari manifold

DOI10.3934/cpaa.2014.13.2289zbMath1304.35257OpenAlexW2322854336MaRDI QIDQ479534

Qing Yuan, Caisheng Chen

Publication date: 5 December 2014

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2014.13.2289

zbMATH Keywords

variational methodNehari manifold\(p\)-Kirchhoff elliptic equation

Mathematics Subject Classification ID

Variational methods for higher-order elliptic equations (35J35) Positive solutions to PDEs (35B09) Singular elliptic equations (35J75) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Multiple solutions for the asymptotically linear Kirchhoff type equations on \(\mathbb{R}^N\) ⋮ Existence of positive solutions for a Schrödinger-Poisson system with bounded potential and weighted functions in \(\mathbb{R}^{3}\) ⋮ Positive solutions for a critical \(p\)-Laplacian problem with a Kirchhoff term ⋮ Liouville-type theorems for stable solutions of Kirchhoff equations with exponential and superlinear nonlinearities ⋮ Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in \(\mathbb R^N\) ⋮ Infinitely many solutions for \(N\)-Kirchhoff equation with critical exponential growth in \({\mathbb {R}}^N\) ⋮ Existence of solutions for a class of singular quasilinear elliptic equations ⋮ A priori bounds and existence of positive solutions to a p-Kirchhoff equations ⋮ Infinitely many solutions forp-Kirchhoff equation with concave-convex nonlinearities in RN

Cites Work

• Unnamed Item
• Multiple solutions for \(p\)-Kirchhoff equations in \(\mathbb R^N\)
• Existence and multiplicity of non-trivial solutions for Schrödinger-Kirchhoff-type equations with radial potential
• Existence of a positive solution to Kirchhoff-type problems without compactness conditions
• Semilinear elliptic equations for beginners. Existence results via the variational approach
• Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(\mathbb R^N\)
• Nonlinear scalar field equations. I: Existence of a ground state
• Ground states of nonlinear Schrödinger equations with potentials
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Nonlinear Schrödinger equations with vanishing and decaying potentials.
• On the existence of positive entire solutions of a semilinear elliptic equation
• Existence of solutions for a class of nonlinear Schrödinger equations with potential vanishing at infinity
• Multiple solutions for the nonhomogeneous Kirchhoff equation on \(\mathbb R^N\)
• On a quasilinear Schrödinger-Kirchhoff-type equation with radial potentials
• Existence of positive solutions to \(p\)-Kirchhoff-type problem without compactness conditions
• Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials
• Multiplicity of high energy solutions for superlinear Kirchhoff equations
• Existence of nontrivial solutions for singular quasilinear elliptic equations on \(\mathbb R^N\)
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity