Existence Of Solutions For Multi-point Boundary Value Problems With High Dimension Kernal At Resonance

This Master's degree thesis is composed of four chapters, which mainly discussed a kind of boundary value problem of second order nonlinear differential equation at resonance and two kinds of boundary value problems of third order nonlinear differential equation at resonance. Our results are different from known results. In this thesis, the existence results are obtained in the case of that the dimension of kernal is 2 or 3. The results of this thesis improve known results and also a new result is obtained.In the first chapter, the historical background of the problem which will be inves-gated and the main results of this thesis are introduced.In chapter 2, by using Mawhin's coincidence degree theory, we establishe a existence result of boundary value problems of second order nonlinear differential eqation with two dimension kernal at resonance. A example is given to ilustrate existence result. The result of this chapter improves known results.In chapter 3 and 4, by using same tools, existence results of two kinds of boundary value problems of third order nonlinear differential equation are established. In chapter 3, existence result of boundary value problems is established in the case of that dimension of kernal is 2. In chapter 4, existence result of boundary value problems is established in the case of that dimension of kernal is 3. Examples are given to illustrate these results. The results of these chapter are new.