Random evolution equations in Frechet spaces

Open Access

Original research article

Author(s):

Saïd Abbas^a, Amaria Arar^a, Mouffak Benchohra^b, Fatima Mesri^b

^a Laboratory of Mathematics, Geometry, Analysis, Control and Applications, Tahar Moulay University of Saïda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria
^b Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 2(3), 128-137.

Received: May 10, 2018

Accepted: August 4, 2018

Published: August 6, 2018

Abstract

This paper deals with the existence of random mild solutions for some classes of first- and second-order evolution equations with random effects in Fréchet spaces. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness.

Keywords: Evolution equation, evolution system, densely defined operator, mild solution, fixed point, Fréchet space.

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APA Style

Abbas, S., Arara, A., Benchohra, M., & Mesri, F. (2018). Random evolution equations in Frechet spaces. Advances in the Theory of Nonlinear Analysis and its Application, 2(3), 128-137.