The Researches On Positive Solutions For Several Kinds Of Periodic Boundary Value Problems

The periodic boundary value problem is an important and classical issue in the theory of differential equations, it has profound practical background and wide range of applications. The main reason is that there are a lot of periodic phenomenon, such as the celestial mechanics, biology, engineering and so on, many periodic phenomenon can be characterized by the periodic boundary value problems, hence the studies of period boundary value problems are valued by many scholars. In many practical problems often only positive solutions are meaningful, so that the periodic boundary value problems have become one of the hot research topics of some scholars.The thesis is structured as follows:The first chapter is an introduction, mainly introduces the research background and significance of the periodic boundary value problems of nonlinear differential equations, and the status of research at home and abroad in recent years.The second chapter introduces the solution of the second kind Fredholm equation by using the Hilbert-Schmidt method, and the solution of its symmetrical kernel is represented with a series of characteristic functions corresponding to homogeneous equation. In addition, it presents how to use the Green’s function to discuss periodic boundary value problems of the ordinary differential equations.The third chapter, on the basis of previous research works, discusses the existence of positive and multiple solutions of the periodic boundary value problems, and proves the existence theorem and multiple solution theorem of positive solutions.The fourth chapter, studies a class of periodic boundary value problems of systems of differential equations, analyses the existence of positive solutions, and explains a concrete example.The fifth chapter is a summary and outlook for this article.