This paper surveys some recent work on a variant of the Mountain Pass Theorem that is applicable to some classes of differential equations involving unbounded spatial or temporal domains. In particular its application to a system of semilinear elliptic PDEs on \(R^n\) and to a family of Hamiltonian systems involving double well potentials will also be discussed.

中文翻译：

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山口定理的一种变体和变分粘着

本文调查了有关山口定理的一个变体的最新工作，该定理适用于涉及无界空间或时间域的某些类型的微分方程。特别是，还将讨论其在\（R ^ n \）上的半线性椭圆PDE系统以及涉及双阱势的哈密顿系统的应用。