Abstract random differential equations with state-dependent delay using measures of noncompactness

Abstract

This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented.

Keywords

• random differential equations
• random mild solution
• state-dependent delay
• measure of noncompactness
• Fréchet spaces