A unified treatment of degenerate nonlocal elliptic problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915887076868096 |
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| author | Gasinski, L. Quoirin, H. Ramos Junior, J. Santos Silva, K. |
| author_facet | Gasinski, L. Quoirin, H. Ramos Junior, J. Santos Silva, K. |
| contents | We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having sublinear or asymptotically linear growth. By combining the study of a suitable auxiliary problem and fixed-point techniques with careful parameter analysis, we establish existence, non-existence, and multiplicity results for positive solutions. Our method reveals sharp parameter thresholds and provides a comprehensive description of the solution set. Finally, for powerlike nonlinearities (including superlinear and singular ones) we provide a more direct approach, based on homogeneity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23077 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A unified treatment of degenerate nonlocal elliptic problems Gasinski, L. Quoirin, H. Ramos Junior, J. Santos Silva, K. Analysis of PDEs We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having sublinear or asymptotically linear growth. By combining the study of a suitable auxiliary problem and fixed-point techniques with careful parameter analysis, we establish existence, non-existence, and multiplicity results for positive solutions. Our method reveals sharp parameter thresholds and provides a comprehensive description of the solution set. Finally, for powerlike nonlinearities (including superlinear and singular ones) we provide a more direct approach, based on homogeneity. |
| title | A unified treatment of degenerate nonlocal elliptic problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.23077 |