Singular Boundary Value Problems Of Non-linear Equation System On A Half-line

In this paper, singular boundary value problems of non-linear equation system on a half-line will be considered.The paper is mainly divided into four chapters.The first section is the introduction of the whole paper. We talk about the background of this paper, and make plans for the research of the problem.The next section consists of definitions and theorems and mainly investigates nonlinear equation systemwhere f,g∈C((0,∞)×R×R, R). We can obtain some conditions for the existence of solutions to singular boundary problems of the above system. By constructing upper and lower solutions we can get the necessary and sufficient conditions for the existence of solutions to singular boundary value problems of quasi-homogenous equation system.where f,g∈C((0,∞)×R~+×R~+,R~+), f(t, 1,1) (?) 0, R~+ = [0,∞), and there are constantsλ,μ,N,M, 0≤λ≤μ< 1, 0 < N≤1≤M, such that for all t>0,u,v≥0and g satisfies the above property.The third section mainly classifies the positive solutions of quasi-homogenous equation system and investigates their existence by applying Schauder-fixed point theorem.At last, we summarize the results of the whole paper.