This paper deals with some recent results for scalar field equations in the case of a potential which converges from above to a limit at infinity. In particular, we shall collect some of the results of the authors which have contributed to partially answer a conjecture of Wei and Yan and we shall announce some results in a forthcoming paper to the aim of giving a short survey which collects the main ideas based on the use of symmetry assumptions and of symmetry methods introduced for the above problem.

中文翻译：

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平面对称和对称约束在某些标量场方程解的存在性证明中的作用

当电势从上方收敛到无穷大时，本文处理标量场方程的一些最新结果。特别是，我们将收集一些对部分回答魏和颜猜想做出贡献的作者的结果，并在即将发表的论文中宣布一些结果，以进行简短的调查，以收集基于以下观点的主要思想针对上述问题引入了对称性假设和对称性方法。