Existence Of Solutions,Positive Solutions And Pseudosymmetric Positive Solutions For Three Classes Of Differential Boundary Value Problems

In this paper, we mainly investigate three classes of differential equations. We divide this article for four chapters. In chapter 1, we narrate the history status quo of the boundary value problems of the differential equation what we researched and the generally way of which we tackled with these problems in our paper. In chapter 2, applying the lower and upper solution method, we study the existence of solutions for a class of fourth-order boundary value problem. And this boundary value problem educes a three-point boundary value problem by the property of the Riemann-Stieltjes integral. Thereby, our result extends the main results in recent papers. Chapter 3 is devoted to studying the existence of positive solutions for a class of nonlinear second-order four-point boundary value problems with alternating coefficient. Our approach relies on the Krasnosel'skii fixed point theorem. The results of this chapter are new and extend previously known results. We use fixed point theorem due to Avery and Peterson to obtain the existence of the triple positive pseudosymmetric solutions for a three-point second-order p-Laplacian integrodifferential boundary value problem in Chapter 4. To the best of our knowledge, this problem has not been studied before.