Positive and negative solutions for a class of Kirchhoff type problems on unbounded domain

DOI10.1016/j.na.2014.07.012zbMath1308.35006OpenAlexW2072828842MaRDI QIDQ2255031

Haining Fan, Xiaochun Liu

Publication date: 6 February 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.07.012

zbMATH Keywords

multiple solutionsnonlocal problemsPalais-Smale sequences

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Quasilinear elliptic equations (35J62) Integro-partial differential equations (35R09)

Related Items (15)

Multiple solutions for the asymptotically linear Kirchhoff type equations on \(\mathbb{R}^N\) ⋮ Existence, nonexistence, and multiple results for the fractional \(p\)-Kirchhoff-type equation in \(\mathbb R^N\) ⋮ Existence and multiplicity of solutions for a class of \(p\)-Kirchhoff-type equation \(\mathbb{R}^N\) ⋮ Existence of solutions for a higher order Kirchhoff type problem with exponential critical growth ⋮ Liouville type theorems for Kirchhoff sub-elliptic equations involving \(\Delta_{\lambda}\)-operators ⋮ Liouville-type theorems for stable solutions of Kirchhoff equations with exponential and superlinear nonlinearities ⋮ Positive and negative solutions for the nonlinear fractional Kirchhoff equation in \(\mathbb{R}^N \) ⋮ Infinitely many solutions for \(N\)-Kirchhoff equation with critical exponential growth in \({\mathbb {R}}^N\) ⋮ \(p\)-fractional Kirchhoff equations involving critical nonlinearities ⋮ Liouville-type theorem for fractional Kirchhoff equations with weights ⋮ Multiple positive solutions for Kirchhoff-type problems in \({\mathbb{R}^3}\) involving critical Sobolev exponents ⋮ Unnamed Item ⋮ Infinitely many solutions forp-Kirchhoff equation with concave-convex nonlinearities in RN ⋮ Multiple positive solutions for degenerate elliptic equations with singularity and critical cone Sobolev exponents ⋮ Multiple positive solutions for a class of Kirchhoff type problems involving critical Sobolev exponents

Cites Work

• Unnamed Item
• Nonlinear perturbations of a periodic Kirchhoff equation in \(\mathbb R^N\)
• Existence of a positive solution to Kirchhoff-type problems without compactness conditions
• Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(\mathbb R^N\)
• The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions
• Multiplicity of solutions for \(p(x)\)-polyharmonic elliptic Kirchhoff equations
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• An existence and stability result for standing waves of nonlinear Schrödinger equations
• Minimax theorems
• Multiple solutions for the nonhomogeneous Kirchhoff equation on \(\mathbb R^N\)
• Multiplicity of solutions for a Kirchhoff equation with subcritical or critical growth.
• Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument
• Local conditions insuring bifurcation from the continuous spectrum
• Positive solutions for a quasilinear elliptic equation of Kirchhoff type
• Sign-changing critical points from linking type theorems
• Existence and multiplicity results for some superlinear elliptic problems on R^N

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