Existence results for differential evolution equations with nonlocal conditions in Banach space

Hedia Benaouda; Johnny Henderson; Berrabah Fatima Zohra

doi:10.26637/MJM0602/0025

Abstract

Our aim in this paper is to study the existence and uniqueness of a mild solution to an initial value problem
(IVP for short) for a class of nonlinear differential evolution equations with nonlocal initial conditions in a Banach
space. We assume that the linear part is not necessarily densely defined and generates an evolution family. We
give two results, the first one is based on a Krasnosel’skii fixed point Theorem, and in the second approach we
make use M¨onch fixed point Theorem combined with the measure of noncompactness and condensing.

Keywords:

Nonlocal initial value problem, evolution family, measure of noncompactness, condensing map, nondensely, v, mild solution, M¨onch fixed point Theorem

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Hedia Benaouda Department of Mathematics, University of Tiaret, PO BOX 78 Zaaroura Tiaret 14000, Algeria. https://orcid.org/0000-0002-7062-5845
Johnny Henderson Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA. https://orcid.org/0000-0001-7288-5168
Berrabah Fatima Zohra Faculty of Exact and Applied Sciences,University of Oran 1, PO BOX 1524, El Mnaouer, Oran 31000, Algeria

Pages: 457-466
Date Published: 01-04-2018
Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)

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