  Concerning a class of diffusive logistic equations, Ni [1, Abstract] proposed
an optimization problem to consider the supremum of the ratio of the L^1 norms
of species and resources by varying the diffusion rates and the profiles of
resources, and moreover, he gave a conjecture that the supremum is 3 in the
one-dimensional case. In [1], Bai, He and Li proved the validity of this
conjecture. The present paper shows that the supremum is infinity in a case
when the habitat is a multi-dimensional ball. Our proof is based on the
sub-super solution method. A key idea of the proof is to construct an L^1
unbounded sequence of sub-solutions.
