Multiplicity results for a semilinear boundary value problem with the nonlinearity crossing higher Eigenvalues

DOI10.1016/0362-546X(85)90058-6zbMath0582.35049MaRDI QIDQ3705836

Alan C. Lazer, Patrick J. McKenna

Publication date: 1985

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

existencemultiplicity of solutionssemilinear boundary value problemnonlinearity crossing higher eigenvalues

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Equations involving nonlinear operators (general) (47J05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items

Multiple solutions for some semilinear elliptic equations, Multiplicity results for asymptotically homogeneous semilinear boundary value problems, On the number of solutions of an elliptic boundary value problem with jumping nonlinearity, A finite element method for computing the bifurcation function for semilinear elliptic BVPs, Existence of unstable periodic solutions for semilinear parabolic equations, Existence of stable and unstable solutions for semilinear parabolic problems with a jumping nonlinearity, The global attractor for a Chafee-Infante problem with source term, Remarks and generalizations related to a recent multiplicity result of A. Lazer and P. McKenna, A Bounded Mountain Pass Lemma Without the (PS) Condition and Applications, Multiple solutions of asymptotically homogeneous problems, Unnamed Item, Multiple solutions of two point boundary value problems with jumping nonlinearities, Some remarks on the number of solutions of some nonlinear elliptic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On nonlinear elliptic problems with jumping nonlinearities
• Variational and topological methods in partially ordered Hilbert spaces
• On the number of solutions of a nonlinear Dirichlet problem
• On the ranges of certain weakly nonlinear elliptic partial differential equations
• On the inversion of some differentiable mappings with singularities between Banach spaces
• A multiplicity result for a class of elliptic boundary value problems
• On nonlinear perturbations which cross the eigenvalues
• On a conjecture related to the number of solutions of a nonlinear Dirichlet problem
• Existence of a third solution for a class of B.V.P. with jumping nonlinearities
• Remarks on some quasilinear elliptic equations
• Nonlinear Integral Equations of the Hammerstein Type