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arXiv · 2202.09442

Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting

Kenichiro Umezu
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Abstract

Let $0 1$ is subcritical, we prove that in the case of $λ_Ω>1$, there exist at least two positive solutions for $λ>0$ sufficiently small but no positive solutions for $λ>0$ large enough. In the case of $λ_Ω<1$, there exists at least one positive solution for every $λ>0$. Here, $λ_Ω>0$ is the smallest eigenvalue of $-Δ$ under the Dirichlet boundary condition. An interpretation of our main results from an ecological viewpoint is presented.

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Kenichiro Umezu. 2022-11-02. Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting. https://arxiv.org/abs/2202.09442

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