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Title

Abstract inclusions in Banach spaces with boundary conditions of periodic type

Authors 1, 1

Affiliations

  1. Faculty of Mathematics and Informatics, Ibn Khaldoun University, 14000 Tiaret, Algeria

Abstract

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ x∈S(x(0),selF(x)) ⎨ ⎩ x (T) = x(0), where, F:[0,T]×→2E∅ is a multivalued map with convex compact values, ⊂ E, selF is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive operators generating not necessarily a compact semigroups.

Keywords

ENG
measure of noncompactness, condensing operator, nonlinear abstract inclusion, accretive operator, integral solution, nonlinear semigroup

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2014/34/2
Export to PBN, Opens in new tab
Pages:
229-253
Main language of publication
English
Received
2014-09-10
Published
2014

DOI: 10.7151/dmdico1164

Exact and natural sciences