Stability of solutions of a 1-dimensional, \(p\)-Laplacian problem and the shape of the bifurcation curve

DOI10.1016/j.na.2020.111757zbMath1442.34042OpenAlexW3005506717MaRDI QIDQ1988384

Bryan P. Rynne

Publication date: 23 April 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.111757

zbMATH Keywords

stability\(p\)-Laplacianbifurcation curve

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Bifurcation theory for ordinary differential equations (34C23) Boundary eigenvalue problems for ordinary differential equations (34B09)

Cites Work

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• Remarks on time map for quasilinear equations
• Multiple positive solutions of the one-dimensional \(p\)-Laplacian
• Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations
• Global bifurcation of steady-state solutions
• Radial solutions of equations and inequalities involving the \(p\)-Laplacian
• Exact multiplicity and ordering properties of positive solutions of a \(p\)-Laplacian Dirichlet problem and their applications.
• Global asymptotic stability of bifurcating, positive equilibria of \(p\)-Laplacian boundary value problems with \(p\)-concave nonlinearities
• Exact multiplicity and stability of solutions of a 1-dimensional, \(p\)-Laplacian problem with positive convex nonlinearity
• Exact multiplicity of solutions and S-shaped bifurcation curves for the \(p\)-Laplacian perturbed Gelfand problem in one space variable
• Sturm--Liouville theory for the p-Laplacian
• Linearized stability implies dynamic stability for equilibria of 1-dimensional, p-Laplacian boundary value problems