Some uniqueness and exact multiplicity results for a predator-prey model
Some uniqueness and exact multiplicity results for a predator-prey model
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DOI：
10.1090/s0002-9947-97-01842-4
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发表时间：
1997
影响因子：
1.3
通讯作者：
Yihong Du;Y. Lou
中科院分区：
文献类型：
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作者：
Yihong Du;Y. Lou
本文考虑一类具有齐次Dirichlet边界条件的捕食者-食饵扩散模型的正解。结果表明，该模型中的某个参数m起着非常重要的作用。当m较大时，对正解的存在性、稳定性和个数有了很好的理解。特别地，我们得到了关于正解的确切个数的各种结果。我们对大m的结果与研究得很好的Casem=0，即经典的Lotka-Volterra捕食者-食饵模型的结果形成了有趣的对比。
In this paper, we consider positive solutions of a predator-prey model with diffusion and under homogeneous Dirichlet boundary conditions. It turns out that a certain parameter m in this model plays a very important role. A good understanding of the existence, stability and number of positive solutions is gained when m is large. In particular, we obtain various results on the exact number of positive solutions. Our results for large m reveal interesting contrast with that for the well-studied casem = 0, i.e., the classical Lotka-Volterra predator-prey model.