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Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. (English) Zbl 1177.34038

Summary: The existence of infinitely many solutions for a Sturm-Liouville boundary value problem is obtained under an appropriate oscillating behavior of the possibly discontinuous nonlinear term. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

MSC:

34B24 Sturm-Liouville theory
34A36 Discontinuous ordinary differential equations
58A05 Differentiable manifolds, foundations
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