Existence and bifurcation theorems for nonlinear elliptic eigenvalue problems of unbounded domains

DOI10.1016/0022-0396(83)90040-2zbMath0506.35081OpenAlexW2054416732MaRDI QIDQ1836805

Hans-Peter Heinz, Achim Bongers, Tassilo Kuepper

Publication date: 1983

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(83)90040-2

zbMATH Keywords

existenceunbounded domainunbounded domainsLjusternik-Schnirelman theorybifurcation from continuous spectrum

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Equations involving nonlinear operators (general) (47J05) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Bifurcations in context of PDEs (35B32)

Related Items

Nodal properties and bifurcation from the essential spectrum for a class of nonlinear Sturm-Liouville problems, Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems, Compact embeddings for weighted Orlicz-Sobolov spaces on \({\mathbb R}^ N\), Asymptotic Formulas for Boundary Layers and Eigencurves for Nonlinear Elliptic Eigenvalue Problems, A hemivariational inequality involving \(p\)-Laplacian on an infinite strip, Bifurcation from the essential spectrum of superlinear elliptic equations, Bifurcation revisited along footprints of Jürgen Scheurle, Bifurcation from the essential spectrum for an elliptic equation with general nonlinearities, Multiple solutions for a class of nonlinear Sturm-Liouville problems on the half line, Uniqueness and bifurcation for solutions of nonlinear Sturm-Liouville eigenvalue problems, A global branch of positive solutions above the continuous spectrum for problems with indefinite nonlinearities, Global bifurcation analysis and uniqueness for a semilinear problem, \(L^q\)-inverse spectral problems for semilinear Sturm-Liouville problems, Unnamed Item, New asymptotic formula for eigenvalues of nonlinear Sturm-Liouville problems, Variational method for precise asymptotic formulas for nonlinear eigenvalue problems, Semilinear elliptic equations on unbounded domains, Multiplicity results for an eigenvalue problem for hemivariational inequalities in strip-like domains, Bifurcation points of a degenerate elliptic boundary-value problem, Global behavior of the branch of positive solutions for nonlinear Sturm-Liouville problems, Some existence and bifurcation results for solutions of nonlinear Sturm- Liouville eigenvalue problems, Weak solutions for a class of semilinear elliptic equations in unbounded domains of ℝ³, An eigenvalue problem for hemivariational inequalities with combined nonlinearities on an infinite strip, Precise spectral asymptotics for nonlinear Sturm-Liouville problems, Nodal properties and variational characterizations of solutions to nonlinear Sturm-Liouville problems, Buckling of a heavy tapered rod.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation when the linearized problem has no eigenvalues
• On the existence of solutions of nonlinear elliptic boundary value problems
• Bifurcation for variational problems when the linearisation has no eigenvalues
• Bifurcation diagrams and periodic solutions to nonlinear equations
• Bifurcation for Neumann problems without eigenvalues
• Über das Verzweigungsverhalten eines nichtlinearen Eigenwertproblems in der Nahe eines unendlich vielfachen Eigenwertes der Linearisierung
• Verzweigung an Eigenwerten unendlicher Vielfachheit - Bemerkungen zu einer Arbeit von H.-P. Heinz
• The lowest point of the continuous spectrum as a bifurcation point
• On the existence and structure of stationary states for a nonlinear Klein-Gordon equation
• Lyusternik-Schnirelman theory and eigenvalue problems for monotone potential operators
• On minimal nonlinearities which permit bifurcation from the continuous spectrum
• Necessary and sufficient conditions for bifurcation from the continuous spectrum
• Bifurcation for Dirichlet Problems Without Eigenvalues
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• Equivalent Norms for Sobolev Spaces
• Embedding Theorems and Quasi-Linear Elliptic Boundary Value Problems for Unbounded Domains
• Some more uniformly convex spaces