Positive solutions to boundary value problems for nonlinear difference equations

The authors consider the second order difference equation Delta(yn-1)(2) + lambda a(n)f(y(n)) = 0, n = 1, 2, ..., T - 1 with the boundary conditions y(0) = y(T) = 0 or y(0) = Delta y(T-1) = 0. Here, T greater than or equal to 2 is an integer, f : [0,infinity) --> [0,infinity) is continuous, a(n) less than or equal to 0, and lambda is a parameter. They give sufficient conditions for these problems to have a positive solution. Examples to illustrate the results and to demonstrate the sharpness of some of the hypotheses are included.