Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity

DOI10.1016/j.jde.2012.02.020zbMath1245.34048OpenAlexW2045739736MaRDI QIDQ424446

Shin-Hwa Wang, Chih-Chun Tzeng, Kuo-Chih Hung

Publication date: 1 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.02.020

zbMATH Keywords

positive solutionglobal bifurcationexact multiplicitytime mapS-shaped bifurcation curvepositone problem

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Parameter dependent boundary value problems for ordinary differential equations (34B08)

Related Items (9)

A global bifurcation theorem for a positone multiparameter problem and its application ⋮ Exact multiplicity of solutions for discrete second order Neumann boundary value problems ⋮ Exact multiplicity of positive solutions of a semipositone problem with concave-convex nonlinearity ⋮ Classification of bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial ⋮ Positive solutions of the one-dimensional \(p\)-Laplacian with nonlinearity defined on a finite interval ⋮ Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications ⋮ Reversed S-shaped bifurcation curve for a Neumann problem ⋮ Classification and evolution of bifurcation curves for a one-dimensional Dirichlet-Neumann problem with a specific cubic nonlinearity ⋮ Global bifurcation and exact multiplicity of positive solutions for the one-dimensional Minkowski-curvature problem with sign-changing nonlinearity

Cites Work

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• Computing the location and the direction of bifurcation
• Global bifurcation of steady-state solutions
• A correction for a paper by J. Smoller and A. Wassermann
• Persistence and bifurcation of degenerate solutions
• Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity and their applications
• Exact multiplicity results for boundary value problems with nonlinearities generalising cubic

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