Abstract: By using the Schauder fixed point theorem and topological degree theory, the author studies the existence of positive solutions of Neumann boundary value problems for second order ordinary differential systems with variable coefficients, where f,g: [0,1]×R→R are continuous functions, and f(x,0)<0, g(x,0)<0; a,b∈C([0,1],[0,∞)) are not always 0 on any subinterval of [0,1]. The result shows that under suitable conditions, there exists λ₀>0 such that the problem has at least one positive solution for 0<λ<λ₀.

Key words: variable coefficient, topological degree theory, semi-positone problem