Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay

Nadjet Abada n65abada@yahoo.fr
Mouffak Benchohra benchohra@univ-sba.dz
Hadda Hammouche h.hammouche@yahoo.fr

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DOI:

https://doi.org/10.4067/S0719-06462010000200001

Abstract

In this paper, we establish sufficient conditions for the existence of mild and extremal solutions for some densely defined impulsive functional differential equations in separable Banach spaces with local and nonlocal conditions. We shall rely for the existence of mild solutions on a fixed point theorem due to Burton and Kirk for the sum of completely continuous and contraction operators, and for the existence of extremal solutions on Dhage‘s fixed point theorem.

Keywords

Densely defined operator , impulsive functional differential equations , fixed point , semigroups , mild solutions , extremal mild solutions , nonlocal condition , separable Banach space

Nadjet Abada Département de Mathématiques, Université Mentouri Constantine, Constantine, Algéria.
Mouffak Benchohra Laboratoire de Mathématiques, Université de Sidi Bel Abbès, BP 89, 22000 Sidi Bel Abbès, Algérie.
Hadda Hammouche Département de Mathematiques, Université Kasdi Merbah Ouargla, Algérie.

Pages: 1–17
Date Published: 2010-06-01
Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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Published

2010-06-01

How to Cite

[1]

N. Abada, M. Benchohra, and H. Hammouche, “Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay”, CUBO, vol. 12, no. 2, pp. 1–17, Jun. 2010.

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Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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