The Problem Of Positive Solution For Two Kinds Of Nonlinear Differential Equations

In this thesis, the existence of positive solutions of two kinds of nonlinear differential equations is considered. One is two-order nonlinear differential equation with integral boundary where αi>0,i=1,…,m-2, and0<ξ1,<ξ2<ξ3<…<ξm-2<1, g is a non-negative integrable function,f∈C([0,1]×[0,+∞),[0,+∞)).The other kind is n-order two-point boundary value problem with a parameter Where n≥2,p∈{1,2,…,n-2}.Firstly, in the chapter1and2, the development and previous research results on two-order and high-order nonlinear differential equations are considered. And we offer some necessary preliminaries.Secondly, in the chapter3, we discuss the existence of positive solution for the equation (1). We use convex function form of cone expansion and compression fixed point theorem to obtain at least one positive solution of equation (1).Thirdly, in the chapter4, we research the existence of positive solution for the equation(2). We use convex function type of cone expansion and compression fixed point theorem to obtain at least one positive solution of equation (2). In the previous literatures, the two kinds of equations were researched by the method of topological degree theory and norm form fixed point theorem of cone expansion and compression. Inspired by many literatures, we use convex function type of cone expansion and compression fixed point theorem to obtain at least one positive solution of equation.