Electron. J. Diff. Eqns., Vol. 2008(2008), No. 69, pp. 1-19.

Perturbed functional and neutral functional evolution equations with infinite delay in Frechet spaces

Selma Baghli, Mouffak Benchohra

Abstract:
This article shows sufficient conditions for the existence of mild solutions, on the positive half-line, for two classes of first-order functional and neutral functional perturbed differential evolution equations with infinite delay. Our main tools are: the nonlinear alternative proved by Avramescu for the sum of contractions and completely continuous maps in Frechet spaces, and the semigroup theory.

Submitted April 15, 2008. Published May 13, 2008.
Math Subject Classifications: 34G20, 34K40.
Key Words: Perturbed functional equation; neutral evolution equations; mild solution; fixed-point theory; nonlinear alternative; Frechet spaces; infinite delay.

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Selma Baghli
Laboratoire de Mathématiques
Université de Sidi Bel Abb&egarve;s
BP 89, 2000 Sidi Bel Abbès, Algérie
email: selma_baghli@yahoo.fr
Mouffak Benchohra
Laboratoire de Mathématiques
Université de Sidi Bel Abb&egarve;s
BP 89, 2000 Sidi Bel Abbès, Algérie
email: benchohra@univ-sba.dz

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