Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910767751626752 |
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| author | Umezu, Kenichiro |
| author_facet | Umezu, Kenichiro |
| contents | For bifurcation analysis, we study the positive solution set for a semilinear elliptic equation of the logistic type, equipped with a sublinear boundary condition modeling coastal fishery harvesting. This work is a continuation of the author's previous studies, where certain results were obtained in a non resonant case, including the existence, uniqueness, multiplicity, and strong positivity for positive solutions. In this paper, we consider the delicate resonant case and develop a sort of non standard bifurcation technique at zero to evaluate the positive solution set depending on a parameter. The nonlinear boundary condition is not right-differentiable at zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case Umezu, Kenichiro Analysis of PDEs For bifurcation analysis, we study the positive solution set for a semilinear elliptic equation of the logistic type, equipped with a sublinear boundary condition modeling coastal fishery harvesting. This work is a continuation of the author's previous studies, where certain results were obtained in a non resonant case, including the existence, uniqueness, multiplicity, and strong positivity for positive solutions. In this paper, we consider the delicate resonant case and develop a sort of non standard bifurcation technique at zero to evaluate the positive solution set depending on a parameter. The nonlinear boundary condition is not right-differentiable at zero. |
| title | Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.04574 |