一类恒化器竞争模型正解存在区域的刻画  

Characterization of existence region of positive solutions for competition model in chemostat

作　　者：刘继远[1] 李艳玲[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《计算机工程与应用》2014年第17期68-73,99,共7页Computer Engineering and Applications

基　　金：国家自然科学基金(No.10971124);教育部博士点专项基金(No.200807180004)

摘　　要：刻画了一类带Ivlev型反应函数的非均匀恒化器竞争模型正解的存在域。利用不动点指数理论和上下解方法证明了在a1λ?1且b1σ?1的前提下,系统有正解的充要条件是a>r1(ab)且b>r2(ab)。结合单调方法和不动点指数理论,说明存在域Λ是R2+中的一个无界连通区域,其边界由两条递增的曲线Γ1:a=F1(b)和Γ2:b=F2(a)构成。证明了系统在存在域Λ的某个子区域内至少有两个正解。The existence region of positive solutions in the unmixed chemostat with the Ivlev response function is por-trayed. It is shown that if a 1λ？1 and b 1σ？1 hold, then the necessary and sufficient conditions, where the system possesses positive solutions, are a＆gt;r1（a、b） and b＆gt;r2（a、b） by using the fixed point theory and the upper and lower solution method. Combining with the monotone method and the fixed point theory, it is proved that Λ is a connected unbounded region in R2＋, whose boundary consists of two monotone nondecreasing curves Γ1：a=F1（b） and Γ2：b=F2（a） . It is shown that the system has at least two positive solutions in certain subregion of Λ.

关 键 词：恒化器 Ivlev型反应函数 不动点指数 单调方法 

分 类 号：O175.26[理学—数学]