Studies On The Solvability Of Two Classes Of Nonlinear Equations

Time delays are often encountered in various practical systems. It has been shown that the existence of delays in a dynamic system may result in instability,oscillations or poor performances. In this thesis, we discuss mainly the existence of solutions for some nonlinear equations. It mainly includes existence of mild solutions for fractional neutral integro-differential equations with delay-dependent state and pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a partial functional differential equation in Banach spaces.This thesis is divided into three chapters.In chapter1, we introduce the research backgrounds and the main results of this thesis.In chapter2, we are mainly concerned with the existence of mild solutions for fractional neutral integro-differential equations with delay-dependent state in the form The main results are obtained by using some suitable fixed point theorem combined with some necessary hypotheses.In chapter3, we are mainly concerned with the existence and uniqueness of pseudo almost automorphic and weighted pseudo almost automorphic mild solutions for a class of partial neutral functional differential equations in the abstract form Under some appropriate assumptions on A,f,g and hi,i=1,2, the existence and uniqueness of pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to the above equations is obtained by using both the Banach contraction mapping principle and fractional powers of operators.