Bifurcation and multiplicity results for critical problems involving the p-Grushin operator
In this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δγp{\Delta }_{\gamma }^{p}. We extend to a generic p>1p\gt 1 a result, which was proved only when p=2p=2. When p≠2p\ne 2, the nonlinear operator −Δγp-{\Delta }_{\gamma...
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De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2025-0089 |
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| author | Malanchini Paolo Bisci Giovanni Molica Secchi Simone |
| author_facet | Malanchini Paolo Bisci Giovanni Molica Secchi Simone |
| author_sort | Malanchini Paolo |
| collection | DOAJ |
| description | In this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δγp{\Delta }_{\gamma }^{p}. We extend to a generic p>1p\gt 1 a result, which was proved only when p=2p=2. When p≠2p\ne 2, the nonlinear operator −Δγp-{\Delta }_{\gamma }^{p} has no linear eigenspaces, so our extension is nontrivial and requires an abstract critical theorem, which is not based on linear subspaces. We use an abstract result based on a pseudo-index related to the Z2{{\mathbb{Z}}}_{2}-cohomological index that is applicable here. We provide a version of the Lions’ concentration-compactness principle for our operator. |
| format | Article |
| id | doaj-art-ae547a99d02e4c93926ebbc53148a481 |
| institution | Kabale University |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-ae547a99d02e4c93926ebbc53148a4812025-08-20T03:40:33ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-08-011414149010.1515/anona-2025-0089Bifurcation and multiplicity results for critical problems involving the p-Grushin operatorMalanchini Paolo0Bisci Giovanni Molica1Secchi Simone2Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, via R. Cozzi 55, I-20125 Milano, ItalyDepartment of Human Sciences and Promotion of Quality of Life, San Raffaele University, via di Val Cannuta 247, I-00166 Roma, ItalyDipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, via R. Cozzi 55, I-20125 Milano, ItalyIn this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δγp{\Delta }_{\gamma }^{p}. We extend to a generic p>1p\gt 1 a result, which was proved only when p=2p=2. When p≠2p\ne 2, the nonlinear operator −Δγp-{\Delta }_{\gamma }^{p} has no linear eigenspaces, so our extension is nontrivial and requires an abstract critical theorem, which is not based on linear subspaces. We use an abstract result based on a pseudo-index related to the Z2{{\mathbb{Z}}}_{2}-cohomological index that is applicable here. We provide a version of the Lions’ concentration-compactness principle for our operator.https://doi.org/10.1515/anona-2025-0089p-grushin operatorcritical exponent35j2035j70 |
| spellingShingle | Malanchini Paolo Bisci Giovanni Molica Secchi Simone Bifurcation and multiplicity results for critical problems involving the p-Grushin operator Advances in Nonlinear Analysis p-grushin operator critical exponent 35j20 35j70 |
| title | Bifurcation and multiplicity results for critical problems involving the p-Grushin operator |
| title_full | Bifurcation and multiplicity results for critical problems involving the p-Grushin operator |
| title_fullStr | Bifurcation and multiplicity results for critical problems involving the p-Grushin operator |
| title_full_unstemmed | Bifurcation and multiplicity results for critical problems involving the p-Grushin operator |
| title_short | Bifurcation and multiplicity results for critical problems involving the p-Grushin operator |
| title_sort | bifurcation and multiplicity results for critical problems involving the p grushin operator |
| topic | p-grushin operator critical exponent 35j20 35j70 |
| url | https://doi.org/10.1515/anona-2025-0089 |
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