纺织高校基础科学学报2017，Vol.30Issue(1)：35-41,7.DOI:10.13338/j.issn.1006-8341.2017.01.007
一类具有交叉扩散的捕食-食饵模型的正解
Positive solutions of a predator-prey model with cross-diffusion
摘要
Abstract
A predator-prey model with cross-diffusion and modified Leslie-Gower type and Holling Ⅱ functional response under Dirichlet boundary conditions is studied.A priori estimate of positive solutions,a necessary and sufficient condition of the existence for positive solutions are derived by making use of maximum principle,Poincaré's inequality and degree theory.It is shown that if the models have positive solutions,then a ＞ λ1,b ＞ λ1;while a ＞ λ,1,λ1(-b/1+βθa)〈0,b〉λ1,λ1(ck2θb-adk1/dk1+dk1k2θb)＜0,the models have positive solutions.关键词
捕食-食饵模型/正解/度理论Key words
predator-prey model/positive solutions/degree theory分类
数理科学引用本文复制引用
张丽霞,李艳玲..一类具有交叉扩散的捕食-食饵模型的正解[J].纺织高校基础科学学报,2017,30(1):35-41,7.基金项目
国家自然科学基金资助项目(11271236,11401356) （11271236,11401356）
