摘要
研究一类带交叉扩散的HollingⅣ捕食-食饵模型在齐次Dirichlet边界条件下正解的存在性.利用极大值原理得到正解的先验估计;借助Crandall-Rabinowitz分歧理论,得出局部分歧正解的存在性,并将局部分歧延拓为全局分歧,得到正解存在的充分条件,从而给出捕食者与食饵在一定条件下可以共存的结构.
This paper concerns the existence of positive solutions for a predator-prey model with cross-diffusion and HollingⅣ under homogeneous Dirichlet boundary conditions.By the maximum principle,apriori estimate of positive solutions are obtained.Then by Crandall-Rabinowitz bifurcation theory,the existence of positive solutions to a local bifurcation is proved.Finally,the local bifurcation is developed to the global one,thus obtaining sufficient conditions of positive solutions,which shows that the predator and the prey can coexist under certain conditions.
出处
《纺织高校基础科学学报》
CAS
2015年第3期287-293,共7页
Basic Sciences Journal of Textile Universities
基金
国家自然科学基金资助项目(11302158)
关键词
捕食-食饵
交叉扩散
先验估计
全局分歧
predator-prey model
cross-diffusion
apriori estimate
global bifurcation
