关于涉及$p$-Grushin算子的临界问题的注记：无限多个解的存在性
A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions
AI总结：
本文研究了涉及$p$-Grushin算子的临界问题，通过截断论证和Krasnoselskii泛数理论，证明了该问题存在无限多个解。
摘要：
我们考虑一个涉及$p$-Grushin算子$Δ_α^p$的临界问题，在有界域中。通过截断论证，我们利用Krasnoselskii的泛数，得到我们问题的无限多个解，将García Azorero和Peral Alonso之前的结论扩展到$p$-Grushin算子。我们分析的核心部分是验证关联函数在一定水平下的Palais-Smale条件。
英文摘要：
We consider a critical problem in a bounded domain involving the $p$-Grushin operator $Δ_α^p$. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of García Azorero and Peral Alonso to the $p$-Grushin operator. A central part of our analysis is the verification of the Palais-Smale condition of the associated functional under a certain level.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
