In this paper, we consider the superlinear Schrödinger equation with bounded potential well. The potential here is allowed to be sign-changing. Without assuming the Ambrosetti–Rabinowitz-type condition, we prove the existence of a nontrivial solution and multiplicity results.

中文翻译：

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具有变号势的非线性薛定ding方程的非平凡解

在本文中，我们考虑势阱有限的超线性Schrödinger方程。这里的潜力被允许改变符号。在不假设Ambrosetti–Rabinowitz型条件的情况下，我们证明了一个非平凡解的存在性和多重结果。