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Eigenfunction branches of nonlinear operators, and their bifurcations

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Author(s): George H. Jr. Pimbley
Series: Lecture Notes in Mathematics
Edition: 1
Publisher: Springer
Year: 1969

Language: English
Pages: 129

front-matter......Page 1
01An example......Page 5
02The extension of branches of solutions for nonlinear equations in Banach spaces......Page 12
03Development of branches of solutions for nonlinear equations near an exceptional point. Bifurcation theory......Page 19
04Solution of the bifurcation equation in the case n=1; bifurcation at the origin......Page 30
05The eigenvalue problem; hammerstein operators; sublinear and superlinear operators; oscillation kernels......Page 44
06On the extension of branches of eigenfunctions; conditions preventing secondary bifurcation of branches......Page 59
07Extension of branches of eigenfunctions of Hammerstein operators......Page 81
08The example of section 1, reconsidered......Page 86
09A two-point boundary value problem......Page 93
10Summary; collection of hypotheses; unsettled questions......Page 103
back-matter......Page 115