On solutions of a class of neutral evolution equations with discrete nonlocal conditions

Abstract

This paper studies the existence, regularity, and asymptotic properties of solutions for a class of neutral differential evolution equations with nonlocal initial conditions on an infinite interval. The existence and regularity of solutions of the considered equation are, respectively, investigated by the theory of fractional power operators and fixed point theorems under some assumptions for nonlinear functions. Then, under suitable conditions, asymptotic properties, including stability and existence of global attracting sets and quasi-invariant sets of mild solutions, are also discussed in the context. Finally, an example is presented to illustrate the applications of the obtained abstract results.