Study On The Boundary-Value Problems Of Ordinary Differential Systems

In this paper, we mainly consider the existence of positive solutions for three-point boundary-value problems "super-sublinear" second-order ordinary differential systems. Here, so-called positive solutions are such solutions whose components are both positive. It is obviously different from usual positive solutions (one of which is positive, while the other is nonnegative ). In order to deal with these problems better, we have an idea that it is to change problems into the fixed point problems of the corresponding compactly continuous mapping on product cone K₁×K₂ ( where K₁,K₂ (?) X ). For this, we apply some fixed point theorems on product cone. First, we recapitulate some fundamental definitions and propositions of topological degrees and some fundamental results about the computation of topological degrees; then, we recapitulate some fixed point theorems on product cone; in the end, by combining some results of positive solutions of three-point boundary-value problem and applying fixed point theorems, we establish the existence of positive solutions.