一类具有扩散的竞争模型正解的多解性和惟一性  

The Multiplicity and Uniqueness of Positive Solutions for a Competition Model with Diffusion

作　　者：王利娟[1] 姜洪领[1] 

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《武汉大学学报（理学版）》2015年第4期308-314,共7页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11201277;11401356);陕西省教育厅科研计划项目(14JK1035;14JK1862);宝鸡文理学院重点科研项目(ZK12043;ZK15038)

摘　　要：讨论了一类带有Beddington-DeAngelis型功能反应函数的竞争模型正解的多解性和惟一性.利用Leray-Shauder度理论、线性算子扰动理论以及标准的椭圆形方程正则性理论得到如下结果:当物种内部竞争系数充分大,且竞争物种的生长率满足一定条件时,该系统或者至少有两个正解或者有惟一正解且该正解渐近稳定.最后通过数值模拟对得到的理论结果进行了验证.The multiplicity and uniqueness of positive solutions for a competition model with Beddington-DeAngelis functional response are discussed.By Leray-Shauder degree theory,linear operator perturbation theory and standard elliptic equations regularity theory,some results obtained are as follows：when the intraspecies competition coefficient is sufficiently large and the growth rates of competition species satisfy certain conditions,the system has either at least two positive solutions or a unique positive solution and it is asymptotically stable.Finally,the theoretical results obtained are verified by the numerical simulation.

关 键 词：竞争模型 多解性 惟一性 数值模拟 

分 类 号：O175.26[理学—数学]