The Existence Of Solutions To Boundary Value Problem For Some Nonlinear Differential Equations

Differential equation boundary value problem is one of the part of differentialequation disciplines, it widely exists in mathematical model of nature, such as springvibration, the population of the ecosystem and so on. Whether ordinary differentialequations or singulary differential equations have a wide rang of applications in thelife.This paper includes the following four chapters.In chapter one, we introduce the background and significance of research, andpresent the use of some basic knowledge.In chapter two, we research the multi-point boundary value problem of three ordernonlinear differential at resonance. In the case of dimensionality of operator Kernelspace is three, using Mawhin coincidence degree, we obtained the existence of thesolution for the problem. And reducing the conditions in the existing literature, andpresenting some supplements about the related literatures.In chapter three, using Mawhin coincidence degree, we discuss the resonanceproblem of second order nonlinear differential equation with generalized Strum-Liouville boundary value problem. Then we obtained the existence of the solution forthe problem, and proved some specific conditions in some literature is not necessary.In chapter four, we introduces two kinds of singular perturbation boundary valueproblem of nonlinear differential equation. Using method of matching and the theory ofdifferential inequalities, we get the existence of the solution for singulary perturbationboundary value problem, and give the uniformly valid asymptotic estimation form.