Here, a nonlocal nonlinear operator known as the fractional $(p,q)$ -Laplacian is considered. The existence of a mountain pass solution is proved via critical point theory and variational methods. To this aim, the well-known theorem on the construction of the critical set of functionals with a weak compactness condition is applied.

中文翻译：

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非局部分数\（（p，q）\）- Laplacian问题的山口解的存在性

在这里，考虑了一个非局部非线性算子，称为分数$（p，q）$ -Laplacian。通过临界点理论和变分方法证明了山口解的存在。为了这个目的，应用了关于具有弱紧凑性条件的关键功能集的构造的众所周知的定理。