| Boundary value problems for ordinary differential equations play a very important role in both theory and applications. They are used to describe a large number of physical, biological and chemical phenomena. Recently, there has been a great deal of research work on boundary value problems for second and higher order differential equations. However, there are very few works on the higher order ordinary differential equations. In this paper we are going to investigate two kinds of more extensive boundary value problems of nth-order differential equations and one kind of more extensive fourth-order boundary-value problem, using the method of lower solution and topology degree theorem, the Krasnosel' skii fixed point theorem and the fixed point index theorem on a cone, we get some new results of the existence of solutions and positive solutions.We divided this paper for four chapters according to the contents.Chapter one is the introduction, 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.Chapter two, by using the method of lower solution and topology degree theorem, we study the existence of positive solutions for singular nth-order boundary value problem with sign changing nonlinearityChapter three, by using the Krasnosel' skii fixed point theorem, we investigate the existence of positive solutions for a class of nonlinear semipositone nth-order boundary value problems.Chapter four, by using the fixed point index theorem on a cone, we study the existence of multiple positive solutions of a class fourth-order boundary-value problem with parameters and second derivative. |
