A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914255517777920 |
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| author | Malanchini, Paolo Bisci, Giovanni Molica Secchi, Simone |
| author_facet | Malanchini, Paolo Bisci, Giovanni Molica Secchi, Simone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions Malanchini, Paolo Bisci, Giovanni Molica Secchi, Simone Analysis of PDEs 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. |
| title | A note on critical problems involving the $p$-Grushin Operator: existence of infinitely many solutions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.09488 |