The structure of Rabinowitz' global bifurcating continua for generic quasilinear elliptic equations

DOI10.1016/S0362-546X(97)00471-9zbMath0901.35007OpenAlexW1968703619MaRDI QIDQ4381321

Bryan P. Rynne

Publication date: 12 November 1998

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

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00471-9

zbMATH Keywords

genericityset of nontrivial solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Bifurcations in context of PDEs (35B32)

Related Items (12)

Genericity of hyperbolicity and saddle-node bifurcations in reaction-diffusion equations depending on a parameter ⋮ Minimal complexity of semi-bounded components in bifurcation theory ⋮ Generic properties of the Rabinowitz unbounded continuum ⋮ Global bifurcation in \(2m\)-order generic systems of nonlinear boundary value problems ⋮ Global bifurcation of positive solutions from zero in nonlinearizable elliptic problems with indefinite weight ⋮ Bifurcation and symmetry breaking of solutions of systems of elliptic differential equations ⋮ Infinitely many turning points for some supercritical problems ⋮ Global bifurcation of positive solutions of semi-linear elliptic partial differential equations with indefinite weight ⋮ Bifurcation from infinity in nonlinear sturm liouville problems with different linearizations at ‘u = ±∞’ ⋮ Solutions of systems of elliptic differential equations on circular domains ⋮ Bifurcation from zero or infinity in Sturm-Liouville problems which are not linearizable ⋮ GLOBAL BIFURCATION FROM INTERVALS IN NONLINEAR STURM-LIOUVILLE PROBLEM WITH INDEFINITE WEIGHT FUNCTION

Cites Work

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• Counterexamples to some conjectures on the number of solutions of nonlinear equations
• Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations
• Smoothness and asymptotics of global positive branches of \(\Delta{} u+ \lambda{} f(u)=0\)
• Preservation of nodal structure on global bifurcation solution branches of elliptic equations with symmetry
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Bifurcation from higher eigenvalues in nonlinear elliptic equations: Continua that meet infinity
• Generic properties of nonlinear boundary value problems
• A Generalization of Multiplicity and the Problem of Bifurcation
• Generic Properties of Eigenfunctions

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