| 一类恒化器竞争模型正解存在区域的刻画 |
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| 引用本文： | 刘继远,李艳玲.一类恒化器竞争模型正解存在区域的刻画[J].计算机工程与应用,2014(17):68-73,99. |
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| 作者姓名： | 刘继远 李艳玲 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 |
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| 基金项目： | 国家自然科学基金（No.10971124）;教育部博士点专项基金（No.200807180004）. |
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| 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a 1λ？1且b 1σ？1的前提下，系统有正解的充要条件是a＆gt;r1（a＆#39;b）且b＆gt;r2（a＆#39;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。
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| 关 键 词： | 恒化器 Ivlev型反应函数 不动点指数 单调方法 |
Characterization of existence region of positive solutions for competition model in chemo-stat |
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| LIU Jiyuan,LI Yanling.Characterization of existence region of positive solutions for competition model in chemo-stat[J].Computer Engineering and Applications,2014(17):68-73,99. |
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| Authors: | LIU Jiyuan LI Yanling |
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| Affiliation: | (College of Mathematics and Information Science, Shaanxi Normal University, Xi＇ an 710062, China) |
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| Abstract: | 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. |
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| Keywords: | chemostat Ivlev response function fixed point index monotone method |
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