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- Title
AN ABSTRACT CAUCHY PROBLEM FOR HIGHER ORDER FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY.
- Authors
Tran Dinh Ke; Obukhovskii, Valeri; Ngai-Ching Wong; Jen-Chih Yao
- Abstract
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.
- Subjects
CAUCHY problem; FUNCTIONAL differential equations; DIFFERENTIAL inclusions; PARTIAL differential equations; BANACH spaces; FIXED point theory
- Publication
Discussiones Mathematicae: Differential Inclusions, Control & Optimization, 2011, Vol 31, Issue 2, p199
- ISSN
1509-9407
- Publication type
Article
- DOI
10.7151/dmdico.1135