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

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Authors :

Hedia Benaouda1*, Johnny Henderson2 and Berrabah Fatima Zohra3

Author Address :

1Department of Mathematics, University of Tiaret, PO BOX 78 Zaaroura Tiaret 14000, Algeria.
2Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA.
3Faculty of Exact and Applied Sciences,University of Oran 1, PO BOX 1524, El Mnaouer, Oran 31000, Algeria.

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"{o}nch fixed point Theorem combined with the measure of noncompactness and condensing.

Keywords :

Nonlocal initial value problem, evolution family, measure of noncompactness, condensing map, nondensely defined operators, mild solution, M"{o}nch fixed point Theorem.



Article Info :

Received : August 21, 2017; Accepted : March 12, 2018.



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