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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2025-0089 |
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| Summary: | 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. |
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| ISSN: | 2191-950X |