In the present paper we initiate the variational analysis of a super sinh-Gordon system on compact surfaces, yielding the first example of non-trivial solution of min-max type. The proof is based on a linking argument jointly with a suitably defined Nehari manifold and a careful analysis of Palais-Smale sequences. We complement this study with a multiplicity result exploiting the symmetry of the problem.

中文翻译：

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紧表面上超sinh-Gordon方程的最小-最大解

在本文中，我们启动了一个在紧凑表面上的超级sinh-Gordon系统的变分分析，给出了最小-最大类型的非平凡解的第一个例子。证明是基于与适当定义的Nehari流形一起的链接参数，以及对Palais-Smale序列的仔细分析。我们利用该问题的对称性对这个结果进行补充，以提供多重结果。