Study For The Existence And Attractivity Of Solutions Of Nonlinear Integral Equations

Integral equations arise from the study of models of chemical, electronicengineering, mechanical, new materials, aerodynamics, neutron transport theory,electromagnetics, transportation, geophysical exploration, population theory, etc.The study on existence and attractivity of the solutions relate to group theory,operator theory, fractal theory, function theory, algebra and many other basicbranches of mathematics.In this paper,by using some new method, we study properties of solutions oftwo kinds of nonlinear integral equations for the frst time.First, using some new drawing conditions for the nonlinear item, we considerthe existence of solutions for the following frst kind of equation, by using haulingback method(see[22-24]), we consider the boundedness of solutions, and provethe frst conclusion,Next, using some new drawing conditions for the nonlinear item, we considerthe existence of solutions for the following second kind of equation, by usinghauling back method(see[22-24]), we consider the attractivity of solutions, andprove the second conclusion.This paper is divided into6chapters. In chapter1, we introduce the researchbackground, the most recent results for properties of solutions of the two kinds ofnonlinear integral equations, our main results,the proving method, the structureof this paper; In chapter2, we introduce some marks which are used in the paper,some defnitions and some lemmas; In chapter3, we consider the properties ofsolutions for the frst kind of equation and prove the frst conclusion; In chapter4, we consider the properties of solutions for the second kind of equation and prove the second conclusion; In chapter5, we give two examples to apply ourconclusions; In chapter6, we summarize the paper.