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Zbl 0998.34024
Davidson, Fordyce A.; Rynne, Bryan P.
Global bifurcation on time scales. (English)
[J] J. Math. Anal. Appl. 267, No.1, 345-360 (2002). ISSN 0022-247X

Summary: The authors 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, they show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and 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.

MSC 2000:: *34B24 Sturm-Liouville theory
34C23 Bifurcation (periodic solutions)

Keywords: solution set; nonlinear Sturm-Liouville boundary value problem; general time scale

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