论文标题
关于扩散逻辑方程的物种与资源之比的无限性
On the unboundedness of the ratio of species and resources for the diffusive logistic equation
论文作者
论文摘要
关于一类扩散的逻辑方程，Ni [1，摘要]提出了一个优化问题，以考虑通过改变资源的扩散率和资源概况的L^1规范和资源的比率，此外，他提出了一个猜想，即一维情况中的至高无上是3。在[1]的Bai中，他和Li证明了这种猜想的有效性。本文表明，在栖息地是多维球的情况下，至上是无穷大的。我们的证明是基于亚super解决方案方法。证据的一个关键思想是构建一个子分析的L^1未绑定序列。
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.
