Random semilinear system of differential equations with impulses

Abstract

Abstract In this paper, we study the existence of solutions for systems of random semilinear impulsive differential equations. The existence results are established by means of a new version of Perov’s, a nonlinear alternative of Leray-Schauder’s fixed point principles combined with a technique based on vector-valued metrics and convergent to zero matrices. Also, we give a random abstract formulation to Sadovskii’s fixed point theorem in a vector-valued Banach space. Examples illustrating the results are included.

Keywords

• random variable
• mild solution
• vector-valued norm
• fixed point theorem
• matrix
• condensing