Existence and Uniqueness Theorem on Uncertain Delay Differential Equation with Local Lipschitz Condition

Uncertain delay differential equation (UDDE) is a type of differential equations driven by Liu process. It has been proved that uncertain delay differential equation has a unique solution in the finite domain, under the conditions that the coefficients are global Lipschitz continuous. This paper will extend this existence and uniqueness theorem from finite domain to infinite domain under the local Lipschitz condition and linear growth condition.