In this paper we consider singularly perturbed nonlinear Schrödinger equations with electromagnetic potentials and involving continuous nonlinearities with subcritical, critical or supercritical growth. By means of suitable variational techniques, truncation arguments and Lusternik–Schnirelman theory, we relate the number of nontrivial complex-valued solutions with the topology of the set where the electric potential attains its minimum value.

中文翻译：

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奇摄动非线性磁薛定ding方程的多重解

在本文中，我们考虑具有电磁势并涉及具有亚临界，临界或超临界增长的连续非线性的奇摄动非线性Schrödinger方程。通过适当的变分技术，截断参数和Lusternik–Schnirelman理论，我们将非平凡复值解的数量与电势达到最小值的集合的拓扑联系起来。