Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 4 (2009), 15 -- 39

CONTROLLABILITY RESULTS FOR SEMILINEAR FUNCTIONAL AND NEUTRAL FUNCTIONAL EVOLUTION EQUATIONS WITH INFINITE DELAY

Selma Baghli, Mouffak Benchohra and Khalil Ezzinbi

Abstract. In this paper sufficient conditions are given ensuring the controllability of mild solutions defined on a bounded interval for two classes of first order semilinear functional and neutral functional differential equations involving evolution operators when the delay is infinite using the nonlinear alternative of Leray-Schauder type.

2000 Mathematics Subject Classification: 34G20; 34K40; 93B05.
Keywords: controllability; existence; semilinear functional; neutral functional differential evolution equations; mild solution; fixed-point; evolution system; infinite delay.

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Selma Baghli Mouffak Benchohra
Laboratoire de Mathématiques, Laboratoire de Mathématiques,
Université de Sidi Bel-Abbès, Université de Sidi Bel-Abbès,
BP 89, 22000 Sidi Bel-Abbès, Algérie. BP 89, 22000 Sidi Bel-Abbès, Algérie.
e-mail: selma_baghli@yahoo.fr e-mail: benchohra@univ-sba.dz

Khalil Ezzinbi
Laboratoire de Mathématiques,
Faculté des Sciences de Semlalia,
BP 2390, Marrakech, Morocco.
e-mail: ezzinbi@ucam.ac.ma

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