Random semilinear system of differential equations with state-dependent delay

Open Access

Original research article

Author(s):

Tayeb Blouhi, Mohamed Ferhat

Faculty of Mathematics and Computer Science, Department of Mathematics, University of Science and Technology Mohamed-Boudiaf El Mnaouar, BP 1505, Bir El Djir 31000, Oran, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 3(1), 1-10.

Received: October 11, 2018

Accepted: December 20, 2018

Published: December 23, 2018

Abstract

In this paper, we establish the existence of mild solutions for a first-order semilinear differential system with state-dependent delay. The existence results are derived by employing a new version of Perov’s fixed point principle, combined with techniques based on vector-valued matrices converging to a zero matrix.

Keywords: Retarded functional differential equations, random variable, state-dependent delay, fixed point theorem.

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APA Style

Mohamed, F., & Tayeb, B. Random semilinear system of differential equations with state-dependent delay. Advances in the Theory of Nonlinear Analysis and its Application, 3(1), 1-10.