Positive Solutions To Multi-point Boundary Value Problems With P-Laplacian Operator

The singular boundary value problem of nonlinear diferential equations is an important research field in diferential equations, which arises in all sorts of applied branch of learning, such as nuclear physics,gas dynamics,fluid mechanics,theory of boundary layer,nonlinear optics and so on. The research on the existence of positive solutions for singular p-Laplacian boundary value problems has brought people's attention and those results have been obtained by using topological degree theory,Schauder fixed point theorem,upper-lower solutions method and shooting method and so on.In chapter one, we introduce a survey to the development of positive boundary value problems. We also summarize main results in the dissertation.In chapter two, we discuss the existence of positive solutions for two-point and three-point boundary value problems with the nonlinearity depending on the first order derivative.In chapter three, we discuss the multiplicity results of positive solutions for three-point boundary value systems with p-Laplacian.