Existence Of Solutions For Neutral Integrodifferential Equations With Nonlocal Conditions

This dissertation is concerned with the existence of mild solutions, strong solutions and strict so-lutions for a class of neutral integrodifferential equations with nonlocal conditions in Banach space. Since the nonlinear term of the systems involves spacial derivatives, the fractional power theory and a-norm is used to discuss the problem. An example is provided to illustrate the application of the obtained results.The dissertation is organized as follows:The Section 2 we recall some notations, concepts, hypotheses and basic results about resolvent operator. In Section 3, we study the existence of mild solutions for Eq.(1) by using fixed point principles. Then, the existence of strong solutions and strict solutions are discussed in section 4 and section 5 respectively. Finally, in Section 6, an example is provided to illustrate the applications of the obtained results.