Constant-sign and sign-changing solutions for nonlinear eigenvalue problems

DOI10.1016/j.na.2007.02.013zbMath1138.35075OpenAlexW2005051595MaRDI QIDQ2482477

Siegfried Carl, Motreanu, Dumitru

Publication date: 17 April 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.02.013

zbMATH Keywords

critical pointsnonlinear eigenvalue problem\(p\)-Laplacianmountain-pass theoremdeformation lemmasign-changing solutionsconstant-sign solutions

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear elliptic equations (35J60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Variational methods for second-order elliptic equations (35J20)

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Cites Work

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• Constant-sign and sign-changing solutions of a nonlinear eigenvalue problem involving the \(p\)-Laplacian.
• A note on a result of Ambrosetti and Mancini
• Sign-changing and multiple solutions for the \(p\)-Laplacian
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• On a class of nonlinear dirichlet problems with multiple solutions
• Sharp nonuniqueness results for some nonlinear problems
• Multiple solutions for a class of semilinear elliptic equations
• Multiple nontrivial solutions for nonlinear eigenvalue problems