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Abstract The fourth-order discrete Dirichlet boundary value problem is also a discrete elastic beam problem. In this paper, the existence of infinitely many solutions to this problem is investigated through the critical point theory. By an important inequality we established and the oscillatory behavior of f either near the origin or at infinity, we obtain the existence of infinitely many solutions, which either converge to zero or unbounded. In the end, two examples are presented to illustrate our results.