Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 13 (2018), 215 -- 235

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EXISTENCE AND ATTRACTIVITY OF SOLUTIONS OF SEMILINEAR VOLTERRA TYPE INTEGRO-DIFFERENTIAL EVOLUTION EQUATIONS

Mouffak Benchohra and Noreddine Rezoug

Abstract. In this paper, we prove a result on the existence and local attractivity of solutions of second order semilinear evolution equation. Our investigations will be situated on the Banach space of functions which are defined, continuous and bounded on the nonnegative real axis. The results are obtained by using the Mönch fixed point and the Kuratowski measure of noncompactness. An example is provided to illustrate the main result.

2010 Mathematics Subject Classification: 45D05; 34G20; 47J35
Keywords: second order semilinear evolution equation; existence of solutions; local attractivity of solutions

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Mouffak Benchohra
Laboratory of Mathematics, University of Sidi Bel Abbès
PO Box 89, Sidi Bel Abbès 22000, Algeria.
e-mail: benchohra@yahoo.com


Noreddine Rezoug
Laboratory of Mathematics, University of Sidi Bel Abbès
PO Box 89, Sidi Bel Abbès 22000, Algeria.
e-mail: noreddinerezoug@yahoo.fr

http://www.utgjiu.ro/math/sma