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