Critical growth problems for polyharmonic operators

DOI10.1017/S0308210500012774zbMath0926.35034MaRDI QIDQ3840003

Gazzola, Filippo

Publication date: 10 August 1998

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

existencesemilinear elliptic problemCarathéodory functionorthogonalizing technique

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40)

Related Items (20)

Multiple solutions for an elliptic system on bounded and unbounded domains ⋮ Existence results for Brezis-Nirenberg problems with Hardy potential and singular coefficients ⋮ Polyharmonic Kirchhoff type equations with singular exponential nonlinearities ⋮ Remainder terms in a higher order Sobolev inequality ⋮ On an elliptic Kirchhoff–Boussinesq type problems with exponential growth ⋮ Existence and nonexistence results of polyharmonic boundary value problems with supercritical growth ⋮ Solutions to Kirchhoff equations with critical exponent ⋮ A critical elliptic problem for polyharmonic operators ⋮ Ground state and multiple solutions for a critical exponent problem ⋮ On Caffarelli-Kohn-Nirenberg-type inequalities for the weighted biharmonic operator in cones ⋮ The critical Neumann problem of Kirchhoff type ⋮ On the quasilinear elliptic problem with a critical Hardy-Sobolev exponent and a Hardy term ⋮ Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights ⋮ Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik–Schnirelman theory ⋮ Positive solutions in semilinear critical problems for polyharmonic operators ⋮ Existence of solutions for singular critical growth semilinear elliptic equations ⋮ Critical polyharmonic problems with singular nonlinearities ⋮ Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth ⋮ The role played by space dimension in elliptic critical problems ⋮ Higher order Brezis-Nirenberg problem on hyperbolic spaces: existence, nonexistence and symmetry of solutions

Cites Work

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• Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents
• On the persistence of the multiplicity of eigenvalues for some variational elliptic operator depending on the domain
• Dual variational methods in critical point theory and applications
• On multiple eigenvalues of selfadjoint compact operators
• Critical exponents, critical dimensions and the biharmonic operator
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• The best sobolev constant
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains
• Solutions of elliptic equations with critical Sobolev exponent in dimension three
• Critical semilinear biharmonic equations in R^N

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