Eigenfunction Branches of Nonlinear Operators, and their Bifurcations

Inhaltsverzeichnis

• An example.
• The extension of branches of solutions for nonlinear equations in Banach spaces.
• Development of branches of solutions for nonlinear equations near an exceptional point. Bifurcation theory.
• Solution of the bifurcation equation in the case n=1; bifurcation at the origin.
• The eigenvalue problem; hammerstein operators; sublinear and superlinear operators; oscillation kernels.
• On the extension of branches of eigenfunctions; conditions preventing secondary bifurcation of branches.
• Extension of branches of eigenfunctions of Hammerstein operators.
• The example of section 1, reconsidered.
• A two-point boundary value problem.
• Summary; collection of hypotheses; unsettled questions.