EXISTENCE OF THREE SOLUTIONS FOR DISCRETE BOUNDARY VALUE PROBLEMS WITH CONTINUOUS-TIME

Using critical point theory, we establish sufficient conditions for the existence of at least three solutions to discrete boundary value problems with continuous-time. Under suitable assumptions on the nonlinearity, we obtain the existence of three positive solutions via the strong maximum principle. To the best of our knowledge, this is the first study of such discrete boundary value problems. Finally, three concrete examples illustrate the main results.