Delay Integral Derivative Containing The Solution And Its Nature

In this thesis, we discuss the existence of the mild solution and the topological properties of solution set to delay integrodifferential inclusions in Banach spaces. It is consisted of two chapters.In the first chapter, we consider the existence of the mild solution to delay integrodifferential inclusions: where A is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators T (t ). The main tools are the theory of operator semigroup in Banach spaces, the properties of Hausdorff's measure of noncompactness and the fixed point techniques. Existence of mild solutions of the equations of different case is obtained without the assumption of compactness on associated semigroup.In the second chapter, we study the topological properties of solution set of delay integrodifferential inclusions.First we consider the delay integrodifferential equations:W ( I 2; X ) = { xφ, f :(φ, f )∈C ([ ? q ,0]; X )×L1 ([0, b ]; X ),xφ,fis the solution of We prove that S (φ, F) is a retract of W (φ),that is, S (φ, F ) ? W(φ)and there exists a continuous functionr such that r ( x )= xfor any x∈S (φ, F).