Existence of solutions to a quasilinear nonlocal PDE
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912152359534592 |
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| author | Carrero, Lisbeth Quaas, Alexander Zuniga, Andres |
| author_facet | Carrero, Lisbeth Quaas, Alexander Zuniga, Andres |
| contents | In this paper, we introduce a new class of quasilinear operators, which represents a nonlocal version of the operator studied by Stuart and Zhou [1], inspired by models in nonlinear optics. We will study the existence of at least one or two solutions in the cone $X=\{u\in H^s_0(Ω): u\geq 0\}$ using variational methods. For this purpose, we analyze two scenarios: the asymptotic sublinear and linear growth cases for the reaction term. Additionally, in the sublinear case, we establish a nonexistence result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of solutions to a quasilinear nonlocal PDE Carrero, Lisbeth Quaas, Alexander Zuniga, Andres Analysis of PDEs 35A01, 35A02, 35A15, 35B09, 35B38, 35R11, 49J45 In this paper, we introduce a new class of quasilinear operators, which represents a nonlocal version of the operator studied by Stuart and Zhou [1], inspired by models in nonlinear optics. We will study the existence of at least one or two solutions in the cone $X=\{u\in H^s_0(Ω): u\geq 0\}$ using variational methods. For this purpose, we analyze two scenarios: the asymptotic sublinear and linear growth cases for the reaction term. Additionally, in the sublinear case, we establish a nonexistence result. |
| title | Existence of solutions to a quasilinear nonlocal PDE |
| topic | Analysis of PDEs 35A01, 35A02, 35A15, 35B09, 35B38, 35R11, 49J45 |
| url | https://arxiv.org/abs/2412.08427 |