Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913846660169728 |
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| author | Gupta, Diksha Sreenadh, Konijeti |
| author_facet | Gupta, Diksha Sreenadh, Konijeti |
| contents | This paper explores the existence of solutions to a class of nonlinear elliptic equations involving a mixed local-nonlocal operator of the form $-Δ_{\mathbb{B}^N} + (-Δ_{\mathbb{B}^N})^s$, with $0 < s < 1$, set in the hyperbolic space $\mathbb{B}^N$. By employing variational methods, we address both subcritical and critical nonlinearities, establishing the existence of weak solutions under appropriate conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12936 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space Gupta, Diksha Sreenadh, Konijeti Analysis of PDEs 35B09, 35B38, 35J20, 35J61, 35R01 This paper explores the existence of solutions to a class of nonlinear elliptic equations involving a mixed local-nonlocal operator of the form $-Δ_{\mathbb{B}^N} + (-Δ_{\mathbb{B}^N})^s$, with $0 < s < 1$, set in the hyperbolic space $\mathbb{B}^N$. By employing variational methods, we address both subcritical and critical nonlinearities, establishing the existence of weak solutions under appropriate conditions. |
| title | Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space |
| topic | Analysis of PDEs 35B09, 35B38, 35J20, 35J61, 35R01 |
| url | https://arxiv.org/abs/2505.12936 |