Solutions for a Kirchhoff type problem with critical exponent in \(\mathbb{R}^N\)

DOI10.1016/j.jmaa.2020.124638zbMath1459.35202OpenAlexW3090493912MaRDI QIDQ2227585

Fen Zhou, Min-Bo Yang

Publication date: 15 February 2021

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.2020.124638

zbMATH Keywords

mountain pass theoremexistence of solutionscritical exponentKirchhoff equation

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations (35J62)

Related Items (3)

A new approach to get solutions for Kirchhoff-type fractional Schrödinger systems involving critical exponents ⋮ Normalized solutions for nonlinear Kirchhoff type equations in high dimensions ⋮ Normalized solutions for nonlinear Kirchhoff type equations with low-order fractional Laplacian and critical exponent

Cites Work

• Critical stationary Kirchhoff equations in \(\mathbb R^N\) involving nonlocal operators
• Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
• \(p\)-fractional Kirchhoff equations involving critical nonlinearities
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional \(p\)-Laplacian in \(\mathbb R^N\)
• Nodal solutions for a Kirchhoff type problem in \(\mathbb{R}^N\)
• Minimax theorems
• The existence of nontrivial solution to a class of nonlinear Kirchhoff equations without any growth and Ambrosetti-Rabinowitz conditions
• Concentration phenomena for a class of fractional Kirchhoff equations in \(\mathbb{R}^N\) with general nonlinearities
• Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains
• Kirchhoff-Hardy fractional problems with lack of compactness
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• Quasilinear asymptotically periodic Schrödinger equations with critical growth

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