EXISTENCE THEORY FOR SINGLE AND MULTIPLE SOLUTIONS TO SINGULAR DISCRETE BOUNDARY VALUE PROBLEMS OF SECOND-ORDER DIFFERENTIAL SYSTEMS

In this paper we establish the existence of single and multiple solutions to the singular discrete boundary value problem    ∆2x(i − 1) + q1(i)f1(i, x(i), y(i)) = 0, i ∈ {1, 2, . . . , T}, ∆2y(i − 1) + q2(i)f2(i, x(i), y(i)) = 0, x(0) = x(T + 1) = y(0) = y(T + 1) = 0, where nonlinear term fk(i, x, y) may be singular at (x, y) = (0, 0), k = 1, 2.