Existence Of Solutions For Second Order Integro-differential Equations In Abstract Space

By using the theory of topological degree, this thesis mainly investigatesthe existence of the boundary and initial value problem of second orderintegro-differential equations in abstract space.In chapter 1, applying the fixed point index theory, we study the existenceof positive solutions for a class of singular boundary value problem of mixedintegro-differential equation in Banach space.In chapter 2, by virtue of H ? Monch fixed point theorem, we investigatethe existence of solutions of initial value problem for second order nonlinearintegro-differential equations on infinite intervals in a Banach space.Two examples are worked out to demonstrate the applications of ourresults.