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Global Bifurcation on Time Scales

✍ Scribed by Fordyce A. Davidson; Bryan P. Rynne

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
130 KB
Volume
267
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider the structure of the solution set of a nonlinear Sturm-Liouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and we show that certain nodal properties of the solutions are preserved along these continua. These results extend the well-known results of Rabinowitz for the case of Sturm-Liouville ordinary differential equations.  2002 Elsevier Science (USA)

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