Existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions

In this paper, we consider the existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions, in which undelayed part admits an operator. We discuss problems by utilizing theory operators, Schauder fixed point theorem Banach theorem. Some new results on considered equation are obtained infinite internal [0,+?). end, applied to a class heat conditions.