Discrete Fourth-order Boundary Value Research Articles

Existence and multiple solutions to a discrete fourth order boundary value problem

In this article, we study a discrete fourth order boundary value problem. By making use of variational methods and critical point theory, we obtain some criteria for the existence and multiple solutions. Moreover, two examples are included to illustrate the applicability of the main results.

Existence of solutions to a discrete fourth order boundary value problem

Criteria are established for the existence of at least two nontrivial solutions to the discrete fourth order boundary value problem where is an integer, , and is continuous in the second argument. Applications of the results to a related eigenvalue problem are also presented. The proofs are mainly based on the variational method and the classic mountain pass lemma of Ambrosetti and Rabinowitz. Examples are included to illustrate the applicability of the results.