Existence and Differentiability of Solutions for Nondensely Defined Neutral Integro-Differential Evolution Equations

This paper is concerned with the existence, continuous dependence and differentiability of solutions for a semilinear neutral integro-differential evolution equation with nonlocal conditions. It is assumed that the linear part of the considered equation is not densely defined but satisfies the resolvent estimates of the Hille–Yosida condition. The results are established by applying the theory of integrated resolvent operators and Banach fixed point theorem. An example is provided in the end to illustrate the applications of the obtained results.