By using variational methods and critical-point theorems, we prove the existence of nontrivial solutions for one-dimensional fourth-order equations. The multiplicity results are also presented.

中文翻译：

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关于一维四阶方程解的存在性

通过使用变分方法和临界点定理，我们证明了一维四阶方程的非平凡解的存在性。还提供了多重性结果。