Multiple solutions for a fourth-order difference boundary value problem with parameter via variational approach

By establishing the corresponding variational framework, and using the mountain pass theorem, linking theorem and Clark theorem in critical point theory, we give the existence of multiple solutions for a fourth-order difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions. Some examples are presented to illustrate the main results.