| 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 L1 norms of species and resource
by varying the diffusion rates and the profiles of resource,
and moreover, he gave a conjecture that the supremum
is 3 in a case when the habitat is a one-dimensional interval.
Recently, Bai, He and Li 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 multi-dimensional ball. |
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