Existence and asymptotic properties of solutions of an integro-differential evolution equation with nonlocal conditions on infinite interval

This paper focuses on the study of existence, regularity and asymptotic properties of solutions for a semilinear neutral integro-differential equation with nonlocal condition. The linear part of the considered equation generates a resolvent operator. The main tools of this consideration are theory of resolvent operators established recently in literature and fixed point theorems. The existence and regularity of solutions on infinite interval of the equation are first investigated by fixed point theorems under compactness condition for the resolvent operator or Lipschitz continuity conditions for the nonlinear functions. Then, the asymptotic properties including stability and asymptotic periodicity of solutions are also discussed here. Finally, two examples are provided to illustrate the applications of the obtained results.