## Global bifurcation on time scales.(English)Zbl 0998.34024

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:

 34B24 Sturm-Liouville theory 34C23 Bifurcation theory for ordinary differential equations
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### References:

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