On a Kirchhoff type problem in \(\mathbb R^N\)

DOI10.1016/j.jmaa.2014.12.017zbMath1312.35110OpenAlexW1993503962MaRDI QIDQ486588

Yuanze Wu, Zeng Liu, Yi Sheng Huang

Publication date: 16 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.12.017

zbMATH Keywords

positive solutionsnontrivial solutionvariational methodsign-changing solutionsKirchhoff type problem

Mathematics Subject Classification ID

Quasilinear elliptic equations (35J62) Positive solutions to PDEs (35B09) Integro-partial differential equations (35R09)

Related Items (14)

Ground state solutions for a class of periodic Kirchhoff-type equation in \({\mathbb{R}}^3\) Involving critical Sobolev exponent ⋮ Multiple solutions for the asymptotically linear Kirchhoff type equations on \(\mathbb{R}^N\) ⋮ On a Kirchhoff equation in bounded domains ⋮ On a \(K\)-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case ⋮ Least energy nodal solution for Kirchhoff type problem with an asymptotically 4-linear nonlinearity ⋮ Positive solutions for the Kirchhoff-type problem involving general critical growth. I: Existence theorem involving general critical growth. ⋮ Existence of ground state solution for a class of one-dimensional Kirchhoff-type equations with asymptotically cubic nonlinearities ⋮ Positive solution for the Kirchhoff-type equations involving general subcritical growth ⋮ On Kirchhoff type equations with critical Sobolev exponent ⋮ Ground state solutions for Kirchhoff type equations with asymptotically 4-linear nonlinearity ⋮ On the existence of least energy solutions to a Kirchhoff-type equation in \(\mathbb{R}^3\) ⋮ On finding solutions of a Kirchhoff type problem ⋮ A study on the critical Kirchhoff problem in high-dimensional space ⋮ Multiplicity of sign-changing solutions for Kirchhoff-type equations

Cites Work

• Nonlinear perturbations of a periodic Kirchhoff equation in \(\mathbb R^N\)
• 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
• The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity.
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function.
• Minimax theorems
• Sign-changing solutions for Schrödinger equations with indefinite supperlinear nonlinearities
• On a class of Kirchhoff type problems
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• Positive solutions for a quasilinear elliptic equation of Kirchhoff type
• Multiplicity of positive and nodal solutions for an inhomogeneous nonlinear elliptic problem
• Existence of positive solutions for nonlinear Kirchhoff type problems in R3 with critical Sobolev exponent
• Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problemviapenalization method

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