Abstract This paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p, q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework. The main features and novelty of the paper are the (p, q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non–degenerate.

中文翻译：

---

退化基尔霍夫 (p, q) - 具有临界非线性的分数系统

摘要 本文讨论临界可能退化的基尔霍夫分数 (p, q) 系统的非平凡解的存在。为清楚起见，结果首先在标量情况下呈现，然后扩展到向量框架中。本文的主要特点和新颖之处在于分数算子的 (p, q) 增长、紧凑性的双重缺乏以及系统可以退化的事实。据我们所知，即使在标量情况下并且考虑的基尔霍夫模型是非退化的，结果也是新的。