Existence of multiple solutions with precise sign information for superlinear Neumann problems

DOI10.1007/s10231-009-0096-7zbMath1188.35057OpenAlexW1978574750MaRDI QIDQ842515

Vasile Staicu, Nikolaos S. Papageorgiou, Sergiu Aizicovici

Publication date: 25 September 2009

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-009-0096-7

zbMATH Keywords

critical groupscritical point theoryNeumann problemnodal solutionsconstant sign solutionsp-laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Construction of pseudo-gradient vector field and sign-changing multiple solutions involving \(p\)-Laplacian
• The spectrum and an index formula for the Neumann \(p\)-Laplacian and multiple solutions for problems with a crossing nonlinearity
• Existence and multiplicity of solutions for Neumann problems
• Every superposition operator mapping one Sobolev space into another is continuous
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Critical point theory and Hamiltonian systems
• Three solutions to a Neumann problem for elliptic equations involving the \(p\)-Laplacian
• \(W^{1,p}\) versus \(C^1\) local minimizers and multiplicity results for quasilinear elliptic equations.
• On a superlinear elliptic \(p\)-Laplacian equation.
• Infinite dimensional Morse theory and multiple solution problems
• Sign-changing and multiple solutions for the \(p\)-Laplacian
• On sign-changing and multiple solutions of the \(p\)-Laplacian.
• Existence of infinitely many weak solutions for a Neumann problem
• Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• A multiplicity theorem for the Neumann \(p\)-Laplacian with an asymmetric nonsmooth potential
• Eigenvalue problems for the \(p\)-Laplacian
• On existence and multiplicity of solutions of Neumann boundary value problems for quasi-linear elliptic equations
• Optimization and nonsmooth analysis
• SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
• Multiple nontrivial solutions for nonlinear eigenvalue problems
• Multiplicity Results for Nonlinear Neumann Problems
• Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• A multiplicity theorem for problems with the \(p\)-Laplacian
• Solution of nonlinear equations having asymptotic limits at zero and infinity.

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