Existence of the Fučík type spectrums for the generalized \(p\)-Laplace operators

DOI10.1016/j.na.2012.01.006zbMath1241.35091OpenAlexW1972492040MaRDI QIDQ765853

Mieko Tanaka

Publication date: 22 March 2012

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.2012.01.006

zbMATH Keywords

Morse theoryquasilinear elliptic equationsconstrained variational problemssecond deformation lemmaFučik spectrum of \(p\)-Laplacian

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62)

Related Items (5)

Nonlinear elliptic equations with a jumping reaction ⋮ Existence of the generalized Fučík spectrum for nonhomogeneous elliptic operators ⋮ Nonlinear Dirichlet problems with a crossing reaction ⋮ Existence of a positive solution for quasilinear elliptic equations with nonlinearity including the gradient ⋮ Generalized eigenvalue problems for \((p,q)\)-Laplacian with indefinite weight

Cites Work

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• Minimax theorems
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• An asymmetric Neumann problem with weights
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• Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator
• Multiple Constant Sign and Nodal Solutions for Nonlinear Neumann Eigenvalue Problems
• Boundary regularity for solutions of degenerate elliptic equations
• Boundary value problems with jumping nonlinearities
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• Strong maximum principles for supersolutions of quasilinear elliptic equations
• Paracompactness and product spaces
• Some remarks on the Fučík spectrum of the \(p\)-Laplacian and critical groups
• On the antimaximum principle and the Fučik spectrum for the Neumann \(p\)-Laplacian

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