Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929215059787776 |
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| author | Umezu, Kenichiro |
| author_facet | Umezu, Kenichiro |
| contents | We study the positive solutions of the logistic elliptic equation with a nonlinear Neumann boundary condition that models coastal fishery harvesting ([18]). An essential role is played by the smallest eigenvalue of the Dirichlet eigenvalue problem, with respect to which a noncritical case is studied in [32]. In this paper, we extend our analysis to the critical case and further study the noncritical case for a more precise description of the positive solution set. Our approach relies on the energy method, sub- and supersolutions, and implicit function analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II Umezu, Kenichiro Analysis of PDEs 35J65 We study the positive solutions of the logistic elliptic equation with a nonlinear Neumann boundary condition that models coastal fishery harvesting ([18]). An essential role is played by the smallest eigenvalue of the Dirichlet eigenvalue problem, with respect to which a noncritical case is studied in [32]. In this paper, we extend our analysis to the critical case and further study the noncritical case for a more precise description of the positive solution set. Our approach relies on the energy method, sub- and supersolutions, and implicit function analysis. |
| title | Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II |
| topic | Analysis of PDEs 35J65 |
| url | https://arxiv.org/abs/2301.12147 |