Local structure of bifurcation curves for nonlinear Sturm-Liouville problems

DOI10.1016/J.JMAA.2010.03.060zbMath1200.34044OpenAlexW2028477208MaRDI QIDQ984709

Tetsutaro Shibata

Publication date: 20 July 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.2010.03.060

zbMATH Keywords

local structurebifurcation curveasymptotic expansion formula

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Sturm-Liouville theory (34B24) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (6)

Asymptotic behavior of the bifurcation diagrams for semilinear problems with application to inverse bifurcation problems ⋮ S-shaped bifurcation curves for nonlinear two-parameter problems ⋮ Global bifurcation and constant sign solutions of discrete boundary value problem involving \(p\)-Laplacian ⋮ Variational methods for NLEV approximation near a bifurcation point ⋮ Asymptotic behavior of bifurcation curve for Sine-Gordon-type differential equation ⋮ Approximation and convergence rate of nonlinear eigenvalues: Lipschitz perturbations of a bounded self-adjoint operator

Cites Work

• Unnamed Item
• A-priori bounds and asymptotics on the eigenvalues in bifurcation problems for perturbed self-adjoint operators
• Remarks on bifurcation for elliptic operators with odd nonlinearity
• Le nombre de solutions de certains problèmes semi-linéaires elliptiques
• Uniqueness of global positive solution branches of nonlinear elliptic problems
• Precise spectral asymptotics for nonlinear Sturm-Liouville problems
• Behavior and stability of positive solutions of nonlinear elliptic boundary value problems arising in population dynamics
• On the global structure of the set of positive solutions of some semilinear elliptic boundary value problems
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Global behavior of the branch of positive solutions to a logistic equation of population dynamics
• On spectral asymptotics and bifurcation for elliptic operators with odd superlinear term
• Upper and lower bounds for eigenvalues of nonlinear elliptic equations: I. The lowest eigenvalue
• Precise asymptotic formulas for semilinear eigenvalue problems

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