一类互惠模型平衡态正解的存在性  

The Existence of Positive Solutions of the Steady State System for Cooperative Model

作　　者：宋倩 李艳玲[1] 袁海龙[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《安徽师范大学学报（自然科学版）》2017年第5期430-437,共8页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金(61672021;11501496);教育部高等学校博士点专项基金(200807180004)

摘　　要：研究了一类带有饱和项的互惠模型在齐次Robin边界条件下平衡态正解的存在性.首先,利用最大值原理得到正解的先验估计;其次,以a为分歧参数,运用局部分歧理论,证明了系统在半平凡解(a*,ηa*,0)和(a',0,ηb)附近出现分歧现象;最后,结合全局分歧理论,将局部分支延拓到无穷.In this paper,the existence of positive solutions for a cooperative model with saturation under homogeneous Robin boundary condition is studied. Firstly,a prior estimates of positive solutions can be established by the maximum principle; Secondly,treating a as a bifurcation parameter,the bifurcations from semi-trivial solutions( a*,ηa*,0) and( a',0,ηb) by the local bifurcation theory; Finally,the local bifurcation solutions can be extended to infinite by the global bifurcation theory.

关 键 词：互惠模型 平衡态正解 全局分歧 

分 类 号：O175.26[理学—数学]