论文标题
关于物种总质量与资源的比率，用于具有差异边界条件的逻辑方程
On the ratio of total masses of species to resources for a logistic equation with Dirichlet boundary condition
论文作者
论文摘要
我们考虑具有均匀Dirichlet边界条件的扩散逻辑方程的固定问题。关于相应的Neumann问题，WEI-MING NI提出了一个问题，如下所示：最大化物种总质量与资源的比率。对于这个问题，BAI，他和Li表明，在一维情况下，比率为3，作者和Kuto表明，在多维球中，上司是无限的。在本文中，我们显示出相同的结果仍然适用于Dirichlet问题。我们的证明是基于次级解决方案方法，并且需要更精细的计算，因为解决方案的存在范围。
We consider the stationary problem for a diffusive logistic equation with the homogeneous Dirichlet boundary condition. Concerning the corresponding Neumann problem, Wei-Ming Ni proposed a question as follows: Maximizing the ratio of the total masses of species to resources. For this question, Bai, He and Li showed that the supremum of the ratio is 3 in the one dimensional case, and the author and Kuto showed that the supremum is infinity in the multi-dimensional ball. In this paper, we show the same results still hold true for the Dirichlet problem. Our proof is based on the sub-super solution method and needs more delicate calculation because of the range of the diffusion rate for the existence of the solution.
