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The authors consider the 2nth-order difference equationwhere f : Z × R → R is a continuous function in the second variable, f (t + T , z) = f (t, z) for all (t, z) ∈ Z × R, r t+T = r t for all t ∈ Z, and T a given positive integer. By the Linking Theorem, some new criteria are obtained for the existence and multiplicity of periodic solutions of the above equation.

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This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type [p n ( x n−1 ) δ ] + q n x δ n = f (n, x n ), where δ > 0 is the ratio of odd positive integers, {p n } and {q n } are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.

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