Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

DOI10.1016/j.jmaa.2010.05.045zbMath1198.35102OpenAlexW1986676246MaRDI QIDQ990853

Jing Zhang, Yu-Wen Wang, Shu-Jie Li, Xiao-Ping Xue

Publication date: 1 September 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.05.045

zbMATH Keywords

semilinear elliptic equationsMorse theoryFucik spectrumNeumann boundary conditionmultiple solutionsjumping nonlinearitydegree theory

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items (3)

Multiplicity results and qualitative properties for Neumann semilinear elliptic problems ⋮ Multiple solutions of \(p\)-Laplacian with Neumann and Robin boundary conditions for both resonance and oscillation problem ⋮ Steklov-Neumann eigenproblems: a spectral characterization of the Sobolev trace spaces

Cites Work

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• Type (II) regions between curves of the Fučik spectrum
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• Mountain pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems
• Splitting theorem, Poincaré--Hopf theorem and jumping nonlinear problems
• Multiple solutions and sign-changing solutions of a class of nonlinear elliptic equations with Neumann boundary condition
• The Fucik spectrum and critical groups
• A Note on the Topological Degree at a Critical Point of Mountainpass-Type
• Ljusternik-Schnirelman theory in partially ordered Hilbert spaces
• Methods in Nonlinear Analysis

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