Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces

J. Henderson, Baylor University, Waco, Texas, U.S.A.
A. Ouahab, Université de Sidi Bel Abbés, Sidi Bel Abbés, Algérie

E. J. Qualitative Theory of Diff. Equ., No. 17. (2005), pp. 1-17.

Abstract: In this paper, a recent Frigon nonlinear alternative for contractive multivalued maps in Fr\'echet spaces, combined with semigroup theory, is used to investigate the existence of integral solutions for first order semilinear functional differential inclusions. An application to a control problem is studied. We assume that the linear part of the differential inclusion is a nondensely defined operator and satisfies the Hille-Yosida condition.

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