EXISTENCE OF SOLUTIONS FOR SINGULAR BOUNDARY-VALUE-PROBLEMS FOR HIGHER-ORDER DIFFERENCE-EQUATIONS

We offer sufficient conditions for the existence of solutions for the boundary value problem Delta(n)y + f(m, y, Delta y,...,Delta(n-2)y) = 0, n greater than or equal to 2, m = 0,1,...,T Delta(i)y(0) = 0, 0 les s than or equal to i less than or equal to n - 3 alpha Delta(n-2)y(0) - beta Delta(n-1)y(0) = 0 gamma Delta(n-2)y(T + 1) + delta Delta(n-1)y (T + 1) = 0 where alpha, beta, gamma and delta are constants satisfyin g alpha gamma(T + 1) + alpha delta + beta gamma > 0, alpha > 0, gamma > 0, beta <greater than or equal to> 0 and delta greater than or equal to gamma.