On the existence of a non-trivial solution for the \(p\)-Laplacian equation with a jumping nonlinearity

DOI10.3836/TJM/1233844055zbMath1175.35056OpenAlexW2021172980MaRDI QIDQ1012435

Mieko Tanaka

Publication date: 21 April 2009

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1233844055

zbMATH Keywords

Morse theoryweak solutionsjumping nonlinearity\(p\)-Laplacian

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20)

Cites Work

• Unnamed Item
• Critical groups and multiple solutions of the \(p\)-Laplacian equations
• Critical point theory and Hamiltonian systems
• Bifurcation for odd potential operators and an alternative topological index
• Existence and multiplicity results for Dirichlet problems with \(p\)-Laplacian.
• Nontrivial critical groups in \(p\)-Laplacian problems via the Yang index
• Infinite dimensional Morse theory and multiple solution problems
• On the Fučík spectrum of the \(p\)-Laplacian
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• Corrigendum: On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• Boundary value problems with jumping nonlinearities
• Nontrivial Solutions forp-Laplace Equations with Right-Hand Side Havingp-Linear Growth at Infinity
• Some remarks on the Fučík spectrum of the \(p\)-Laplacian and critical groups
• Solution of nonlinear equations having asymptotic limits at zero and infinity.

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