The Existence Of Solutions To Several Classes Of Nonlinear Ordinary Differential Equations With Integral Boundary Conditions

The study of differential equation boundary value problems is a classical research topic with a wide range of applications in many fields,such as cybernetics,economics,elasticity,traffic flow,physics,chemistry,biology,biophysics,seismic detection,signal and image processing,electromagnetism,and materials science.The proposed theory of differential equations provides an important solution to these problems and provides a very suitable mathematical model for the solution of these problems.The qualitative study of solutions to boundary value problems of differential equations is very important,as only by first proving the existence and number of solutions can the equations be solved numerically and applied in practice,thus completing the analysis and solution of practical problems.Therefore,the study of the existence of solutions to boundary value problems using the theory of nonlinear generalized functional analysis has attracted the attention of many mathematical researchers,especially in home and abroad.This paper is divided into five chapters as follows.The first chapter briefly introduces the background and current status of the research on the boundary value problem of ordinary differential equations,then explains the main content of this paper.The second chapter investigates the existence of solutions of third-order differential equations with integral boundary conditions,which are obtained in the text by using monotone iterations.The third chapter considers the integral boundary value problem with parameters,and this chapter obtains the existence of solutions to this boundary value problem and the range of values of the parameters by using the Guo-Krasnosel’skii fixed point theorem.The fourth chapter investigates the existence of solutions to a system of fractional order differential equations with coupled integral boundary conditions.Firstly,the fractional differential system which we research is transformed into an equivalent integral operator,and then sufficient conditions for the existence of a unique solution to the system are obtained by the Banach contraction mapping principle,and the existence of a solution to this system is obtained via the alternative theorem of Leray-Schauder.The fifth chapter discusses the semipositone integral fractional order boundary value problem,and this chapter continues to use the nonlinear alternative of Leray-Schauder type to prove the existence of solutions to this semipositione problem.