Critical groups and multiple solutions of the \(p\)-Laplacian equations

DOI10.1016/j.na.2004.08.012zbMath1153.35322OpenAlexW1970468554MaRDI QIDQ703422

Mei Yue Jiang

Publication date: 11 January 2005

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.2004.08.012

zbMATH Keywords

critical groupsmultiple solutions\(p\)-Laplacian

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (16)

Sign-changing and constant-sign solutions for \(p\)-Laplacian problems with jumping nonlinearities ⋮ Some qualitative results of the critical groups for the \(p\)-Laplacian equations ⋮ Three nontrivial solutions of boundary value problems for semilinear $\Delta_{\gamma}-$Laplace equation ⋮ Nonhomogeneous nonlinear Dirichlet problems with a \(p\)-superlinear reaction ⋮ Multiple solutions for the p-Laplacian equations with concave nonlinearities via Morse theory ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík type resonance at infinity. II ⋮ Applications of Morse theory to some nonlinear elliptic equations with resonance at zero ⋮ Sign-changing solutions of nonlinear elliptic equations ⋮ A remark on the Ambrosetti-Prodi type problem ⋮ Critical groups at infinity for \(p\)-Laplacian equations with indefinite nonlinearities ⋮ Existence of solutions to a class of \(p\)-Kirchhoff equations via Morse theory ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík type resonance at infinity ⋮ On the existence of a non-trivial solution for the \(p\)-Laplacian equation with a jumping nonlinearity ⋮ Some bifurcation results and multiple solutions for the \(p\)-Laplacian equation ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík-type resonance at infinity. III ⋮ Critical groups at zero and multiple solutions for a quasilinear elliptic equation

Cites Work

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• Construction of pseudo-gradient vector field and sign-changing multiple solutions involving \(p\)-Laplacian
• Asymmetric elliptic problems with indefinite weights
• On a superlinear elliptic equation
• Type II regions between curves of the Fučik spectrum and critical groups
• Remarks on multiple solutions for asymptotically linear elliptic boundary value problems
• The Conley index and the critical groups via an extension of Gromoll-Meyer theory
• On the existence of sign changing solutions for semilinear Dirichlet problems
• On a superlinear elliptic \(p\)-Laplacian equation.
• On the Morse indices of sign changing solutions of nonlinear elliptic problems
• Mountain pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems
• Infinite dimensional Morse theory and multiple solution problems
• On sign-changing and multiple solutions of the \(p\)-Laplacian.
• Dirichlet problem with indefinite nonlinearities
• On the Fučík spectrum of the \(p\)-Laplacian
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• Resonance problems for the \(p\)-Laplacian
• The Fucik spectrum and critical groups
• MULTIPLE SOLUTIONS TO p-LAPLACIAN PROBLEMS WITH ASYMPTOTIC NONLINEARITY AS up−1 AT INFINITY
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero
• Ljusternik-Schnirelman theory in partially ordered Hilbert spaces
• Some remarks on the Fučík spectrum of the \(p\)-Laplacian and critical groups
• Asymptotically linear Dirichlet problem for the \(p\)-Laplacian
• Critical point theory on partially ordered Hilbert spaces
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian

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