Multiplicity of solutions for a fourth order elliptic equation with critical exponent on compact manifolds

DOI10.1016/j.aml.2006.06.002zbMath1152.35350OpenAlexW2045852184MaRDI QIDQ868021

Mohammed Benalili

Publication date: 19 February 2007

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2006.06.002

zbMATH Keywords

fourth order elliptic equationcritical Sobolev growth

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Critical exponents in context of PDEs (35B33) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for higher-order elliptic equations (35J35)

Related Items (9)

Multiple solutions for a class of nonhomogeneous fourth-order quasilinear equations with nonlinearities ⋮ Ground states for a class of asymptotically linear fourth-order elliptic equations ⋮ High energy solutions and nontrivial solutions for fourth-order elliptic equations ⋮ Infinitely many small energy solutions for fourth-order elliptic equations with \(p\)-Laplacian in \(\mathbb{R}^N\) ⋮ Existence and multiplicity of solutions for a class of fourth-order elliptic equations in \(R^N\) ⋮ Solutions of biharmonic equations with mixed nonlinearity ⋮ Infinitely many solutions for fourth-order elliptic equations with general potentials ⋮ Infinitely many solutions for fourth-order semilinear \(\Delta_{\gamma}\)-Laplace equation in \(\mathbb{R}^N\) ⋮ Existence and non-existence of solutions for semilinear bi-\(\Delta_{\gamma}\)-Laplace equation

Cites Work

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• Elliptic equations of fourth-order with critical exponents on compact Riemannian manifolds
• Critical exponents, critical dimensions and the biharmonic operator
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals

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