On a mild solution of a semilinear functional‐differential evolution nonlocal problem

The existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional‐differential evolution equation in a general Banach space are studied. Methods of a C0 semigroup of operators and the Banach contraction theorem are applied. The result obtained herein is a generalization and continuation of those reported in references [2‐8].