A new existence and uniqueness theorem for uncertain delay differential equations

Abstract

Uncertain delay differential equations are a type of differential equations driven by a Liu process. So far, it has been proved that uncertain delay differential equation has a unique solution in the finite domain, in which its coefficients satisfy the global Lipschitz continuity. This paper continues to focus on the existence and uniqueness of the solutions of uncertain delay differential equations on the infinite domain. Meanwhile, a new existence and uniqueness theorem for uncertain delay differential equations under one-sided local Lipschitz condition and linear growth condition is deduced.