Existence And Attractivity Of Solutions Of A Volterra Integral Equation

In this thesis,we discuss existence and attractivity of solutions of a Volterra integral equation.The thesis is organized as follows.In Chapter 1,we introduce the backgrounds of the problem and the main results of this thesis.In Chapter 2,we mainly study existence of solutions of the following Volterra integral equation by using the theory of measure of noncompactness:u(t)= p(t)+ g(t,u(t))f0,t a(t-s)f(t,s,u(s))ds,t ?[0,T],where T>0.In Chapter 3,we mainly investigate existence and attractivity of the following Volterra integral equation combining the theory of noncompactness and Schauder fixed point theorem:u(t)= p(t)+ g(t,u(t))f0,ta(t-s)f(t,s,u(s))ds,t>0.