Existence Of Solutions For Nonlinear Differential-integral Equations

With the rapid development of science and technology,nonlinear equations have played an important role in various fields such as physics,engineering,and economics.Many practical problems can be described by nonlinear equations.In this paper,we study the existence of solutions to nonlinear differential equations by using some methods of nonlinear functional analysis,such as cone theory,fixed point index theorem,fixed point theorem,operator theory,etc.The full text is divided into three chapters.That is,the main contents are as follows:In Chapter 1,we introduce the research significance of nonlinear equations and the research status at home and abroad.Then we briefly discuss the main results of this paper.In Chapter 2,we study the second-order nonlinear periodic boundary value problem with two parameters(?) First,we establish a Banach space and use Arzela-Ascoli theorem to solve the problem of the lack of compactness of the equation in the Banach space.Then,we assume certain conditions and obtain the existence result of the solution of the problem by using fixed point index theorem.Finally,we give an example to illustrate the effectiveness of the main results.In Chapter 3,we study the integral equation of the following form(?) we adopt a more concise method than the previous literature to prove the existence of solutions.