Positive high energy solution for Kirchhoff equation in \(\mathbb{R}^{3}\) with superlinear nonlinearities via Nehari-Pohožaev manifold

DOI10.3934/dcds.2015.35.3857zbMath1311.35113OpenAlexW2329227937MaRDI QIDQ2260749

Hongyu Ye

Publication date: 12 March 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.3857

zbMATH Keywords

Kirchhoff equationsuperlinear nonlinearitiesbarycenter mapNehari-Pohožaev type manifold

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Positive solutions to PDEs (35B09)

Related Items

Ground state solutions for Kirchhoff-type equations with general nonlinearity in low dimension, The mass concentration phenomenon for \(L^2\)-critical constrained problems related to Kirchhoff equations, An autonomous Kirchhoff-type equation with general nonlinearity in \(\mathbb{R}^N\), Three solutions for a new Kirchhoff-type problem, Non-degeneracy of single-peak solutions to a Kirchhoff equation, Multiplicity of positive solutions for Kirchhoff type problems in \(\mathbb{R}^3\), On positive ground state solutions for the nonlinear Kirchhoff type equations in ℝ³, Positive solutions of a superlinear Kirchhoff type equation in \(\mathbb{R}^N\) \((N \geq 4)\), Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ³, Ground states for Kirchhoff equation with Hartree-type nonlinearities, Existence of solution for an asymptotically linear Schrödinger-Kirchhoff equation, The number of positive solutions affected by the weight function to Kirchhoff type equations in high dimensions, On some nonlocal equations with competing coefficients, Existence of positive solution for the nonlinear Kirchhoff type equations in the half space with a hole, Positive solutions for Kirchhoff equation in exterior domains, A singularly perturbed Kirchhoff problem revisited, On the Kirchhoff type equations in \(\mathbb{R}^N \)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of a positive solution to Kirchhoff-type problems without compactness conditions
• Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth
• Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(\mathbb R^N\)
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• Infinitely many radial solutions for Kirchhoff-type problems in \(\mathbb{R}^N\)
• Regularity for a more general class of quasilinear equations
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• Minimax theorems
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• Three nodal solutions of singularly perturbed elliptic equations on domains without topology
• Multiplicity of high energy solutions for superlinear Kirchhoff equations
• Existence of positive solutions for nonlinear Kirchhoff type problems in R3 with critical Sobolev exponent
• Existence of solutions with prescribed norm for semilinear elliptic equations
• Radial symmetry of positive solutions of nonlinear elliptic equations in Rⁿ
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Some properties of weak solutions of nonlinear scalar field equations
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• On the Well-Posedness of the Kirchhoff String
• On harnack type inequalities and their application to quasilinear elliptic equations
• Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation