Abstract: By using the fixed-point theorem of Krasnoselskii, we give the existence of positive solutions for a class of discrete beam equations with nonlinear boundary conditions, where λ>0 is a parameter, h: ［2,T］_Z→［0,∞) is function, f: (0,∞)→R is continuous, and allows singularity at u=0, grows superlinearly at u=∞.

Key words: nonlinear boundary condition, positive solution, Lebesgue dominated convergence theorem, superlinear growth