Existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in banach spaces and applications

This paper investigates the existence of global solutions for initial value problems of the nonlinear integrodifferential equations in Banach spaces. We obtain the existence of global solutions by Schauderʹs fixed-point theorem. Our results are the generalizations and improvements of recent results. As applications of our results, the existence of global solutions of two classes of third-order mixed boundary value problem is obtained, and an example of infinite system for nonlinear integrodifferential equations is worked out to illustrate our main results.