Two-point Boundary Value Problems Of Third-order Differential Difference Equations

This paper mainly applies the techniques of differential inequality and the theory of upper and lower solution theory to study Two-point boundary value problems of a class of Third-order nonlinear differential difference equations under certain conditions. This article is based on the existing results of boundary value problems for second-order differential equation to set up the existence of a second-order differential Volterra Integral Differential Equations, and then applies reduction to absurdity to prove the uniqueness of the solution. On the appropriate conditions, it concludes the existence of a class derived third-order differential difference equations.On the basis of singular perturbation of the third-order boundary value solution problem, also with the upper and lower solutions, and on the appropriate conditions, it constructs the appropriate upper and lower solutions, and studies the existence of solutions and singular perturbation of a certain third order nonlinear differential equations set boundary value problems for differential.This paper is mainly divided into three parts:The first part, it mainly introduces the origins and the development of the theory on differential equations and some conclusions, which have been drawn by the predecessors. The theoretical basis of the main body is given below, for example:upper and lower solutions, Nagumo condition, Schauder fixed-point theory, and the basic result of differential inequality is also supplied.The second part, it uses a differential inequality techniques, and constructs appropriate upper and lower solutions under certain conditions; meanwhile, studies the singularly perturbed problems of the individual third-order nonlinear differential difference equations.The third part, based on the perturbation theory of the odd single third-order differential boundary value problems of nonlinear differential study in the second part, it uses the method of the upper and lower solution, under appropriate conditions, to construct the appropriate upper and lower solutions. At the same time, it studies the existence of solutions and singular perturbation of a certain third order nonlinear differential equations boundary value problems for differential.