An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

Ke, Tran ; Obukhovskii, Valeri ; Wong, Ngai-Ching ; Yao, Jen-Chih

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 31 (2011) no. 2, pp. 199-229.

Résumé

The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.

Détail

Keywords: Cauchy problem, functional differential inclusion, infinite delay, higher order, existence family, phase space, fixed point, multivalued map, measure of noncompactness, condensing map

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