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BVP for Carathéodory inclusions in Hilbert spaces: sharp existence conditions and applications. (English) Zbl 1276.34013
Summary: This article concerns an existence result for Floquet boundary value problems associated to semilinear differential inclusions with Carathéodory right hand side in a Hilbert space. We apply a continuation principle and we require a sharp (i.e., localized on the boundary) transversality condition. We give an application to a nonlinear partial differential inclusion with periodic conditions.

MSC:
34A60 Ordinary differential inclusions
34B15 Nonlinear boundary value problems for ordinary differential equations
35R70 PDEs with multivalued right-hand sides
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