Existence Of Solutions Of Integro-Differential Equations In Banach Spaces

In this paper, we firstly consider the following periodic boundary value problems (for short PBVP) and obtain an existence theorem of extremal solutions by using the upper and lower method. The result obtained improves and generalizes some known results.Second, the minimal and maximal solutions of initial value problems (for short IVP) of the nonlinear second order mixed type integro-differential equation in Banach spaces are investigated by using new comparison principle and partial order method. The results presented here essentially improve, generalize and unify some known results.