Existence of nontrivial solutions to a critical fourth-order Kirchhoff type elliptic equation

DOI10.1007/s10440-024-00668-9zbMATH Open1546.3505MaRDI QIDQ6596324

Qian Zhang, Yuzhu Han

Publication date: 2 September 2024

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

existenceNeumann problemfourth-order Kirchhoff-type equation

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations (35J62)

Cites Work

• Unnamed Item
• Existence and multiplicity of solutions for a fourth-order elliptic equation
• Solutions to Kirchhoff equations with critical exponent
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Minimax theorems
• Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument
• Existence and nonexistence of nontrivial solutions for critical biharmonic equations
• Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent
• Existence of solutions for fourth order elliptic equations of Kirchhoff type
• Multiplicity of solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Initial-boundary value problems for an extensible beam
• Critical exponents, critical dimensions and the biharmonic operator
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Existence and nonexistence of solutions to a critical biharmonic equation with logarithmic perturbation
• Weighted fourth order equation of Kirchhoff type in dimension 4 with non-linear exponential growth
• Weighted second order Adams inequality in the whole space \(\mathbb{R}^4\)

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