Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions

DOI10.1017/S030821050003136XzbMath0724.35041MaRDI QIDQ5758559

Filomena Pacella, Massimo Grossi

Publication date: 1990

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

zbMATH Keywords

Palais-Smale conditionpositive solutionsmixed boundary conditionscritical Sobolev exponent

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65)

Related Items (18)

High energy positive solutions of Neumann problem for an elliptic system of equations with critical nonlinearities ⋮ The role of the boundary in some semilinear Neumann problems ⋮ A class of solutions for the Neumann problem \(-\Delta u+ \lambda u= u^{(N+2)/ (N-2)}\) ⋮ High energy positive solution for mixed and Neumann elliptic problems with critical nonlinearity ⋮ Positive solutions to a Neumann problem of semilinear elliptic system with critical nonlinearity ⋮ A nonlocal concave-convex problem with nonlocal mixed boundary data ⋮ Existence of nonradial positive and nodal solutions to a critical Neumann problem in a cone ⋮ Existence and multiplicity results in the presence of symmetry for elliptic equations with critical Sobolev exponent ⋮ Multiple solutions of an inhomogeneous Neumann problem for an elliptic system with critical Sobolev exponent ⋮ Condensation of least-energy solutions: The effect of boundary conditions ⋮ Existence of two solutions of nonlinear elliptic equations with critical Sobolev exponents and mixed boundary conditions ⋮ On the pure critical exponent problem for the \(p\)-Laplacian ⋮ Positive solutions for singular elliptic equations with mixed Dirichlet-Neumann boundary conditions ⋮ A nonexistence theorem for an equation with critical Sobolev exponent in the half space ⋮ High-energy positive solutions for a critical growth Dirichlet problem in noncontractible domains ⋮ Serrin's type overdetermined problems in convex cones ⋮ On the critical Neumann problem with weight in exterior domains. ⋮ Overdetermined problems and constant mean curvature surfaces in cones

Cites Work

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• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Convergence of solutions of H-systems or how to blow bubbles
• Best constant in Sobolev inequality
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Existence and non-existence results for semilinear elliptic problems in unbounded domains

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