带有源自沿海渔业捕捞的非Lipschitz非线性边界条件的扩散逻辑斯蒂方程：共振情形
Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case
AI总结：
本文研究沿海渔业捕捞模型对应的带次线性边界条件的逻辑斯蒂型椭圆方程，在共振情形下发展零点处非标准分支技术，刻画依赖参数的正解集。
摘要：
为了进行分支分析，我们研究了一类逻辑斯蒂型半线性椭圆方程的正解集，该方程配备了一个模拟沿海渔业捕捞的次线性边界条件。本工作是作者此前研究的延续，此前已在非共振情形下获得了若干结果，包括正解的存在性、唯一性、多重性和强正性。在本文中，我们考虑微妙的共振情形，并发展了一种在零点处的非标准分支技术，以评估依赖于一个参数的正解集。该非线性边界条件在零点处不是右可微的。
英文摘要：
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.
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