| Abstract: |
| This talk is concerned with a class of stationary logistic equations for which Ni proposed an optimization problem to consider the supremum of the ratio of the total masses of species to resources by varying the diffusion rates and the configuration of resources, and moreover, he gave a conjecture that the supremum is 3 in a case when the habitat is a one-dimensional interval. Concerning this conjecture, Bai, He and Li (2016) found a sequence of diffusion rates and resource functions to make the corresponding ratios tend to the supremum 3 from below. In this talk, we first show the asymptotic profile of species corresponding to the maximizing sequence found by Bai et al. Next, we introduce a result that the supremum is infinity in a case when the habitat is a general multi-dimensional domain. |
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