Abstract: By using  Jensen’s inequality of nonnegative upper convex function and the fixed point index theory, we discuss the existence of positive solutions of the boundary value problem for a class of nonlinear difference equations, and obtain sufficient conditions for the existence of positive solutions of the Dirichlet boundary value problem for the second order difference equations, where ［1,T］_Z∶={1,2,…,T}, T≥2 is the integer, Δu(t)=u(t+1)-u(t) is the forward difference operator, f,g: ［1,T］_Z×［0,∞)×［0,∞)→［0,∞) are continuous.

Key words: Jensen’s inequality, positive solution, second-order difference equation, fixed point index theory