A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions

Paolo Malanchini; Giovanni Molica Bisci; Simone Secchi

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arXiv · 2601.09488

A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions

Paolo Malanchini·Giovanni Molica Bisci·Simone Secchi

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Abstract

We consider a critical problem in a bounded domain involving the $p$-Grushin operator $\Delta_\alpha^p$. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of Garc\'ia 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.

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Paolo Malanchini, Giovanni Molica Bisci, Simone Secchi. 2026-01-14. A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions. https://arxiv.org/abs/2601.09488

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