The Existence Of Solutions Of Integro-differential Equations In Banach Space And Monotone Iterative Techniques

In the first chapter ,the following initial value problems (IVP) for second order mixed integro-differential equations in Banach space are considered :Suppose that the following assumptions are satisfiedpactness of a bounded subset in E.We consider the situation that the lower solution is less than the upper solution.First we prove a comparison result .Then by using the theory of cone and the monotone iterative technique, we have obtained the existence of the minimal and maximal solutionsTheorem 1.3.2 Assume that E is a real Banach space,P is a regular cone,arid (Hl),(H2)are satisfied.PurtherIn the second chapter ,we consider the periodic boundary value problems (PBVP) for second order integro- differential equations in a Banach space under the weak* topology. We give the following assumptions:In this paper,we give the integration expressions of the solutions .And we considered two different situations that the lower solution is less than the upper solution and the lower solution is no less than the upper solution.First of all we prove a comparison result . The main assumptions are following:...