一类具有扩散的竞争模型正解的多解性和惟一性

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 王利娟 WANG Lijuan 1 first-author 姜洪领 JIANG Hongling 1 宝鸡文理学院数学与信息科学学院 宝鸡文理学院数学与信息科学学院 Institute of Mathematics and Information Science,Baoji University of Arts and Sciences Institute of Mathematics and Information Science,Baoji University of Arts and Sciences 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. 竞争模型 多解性 惟一性 数值模拟 competition model multiplicity uniqueness numerical simulation 10.14188/j.1671-8836.2015.04.002 O175 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） 2015-04-01 2021-03-31 4 61