具协作捕食的扩散捕食者-食饵系统的非常值稳态解  

Nonconstant stationary solutions of a diffusive predator-prey systemwith hunting cooperative

作　　者：陈婧 隋光宇 赵治涛[1] CHEN Jing;SUI Guang-yu;ZHAO Zhi-tao(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China;Chengdu No.7 High School,Chengdu 610000,China)

机构地区：[1]黑龙江大学数学科学学院,黑龙江哈尔滨150080 [2]成都市第七中学,四川成都610000

出　　处：《东北师大学报（自然科学版）》2020年第2期46-51,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11201128);黑龙江省自然科学基金资助项目(A201414).

摘　　要：主要研究了具协作捕食的扩散捕食者-食饵系统的非常值稳态解问题.基于最大值原理和Harnack不等式,建立了系统非常值正解的先验估计.利用Poincaré不等式,给出了系统非常值稳态解的不存在性.基于Leray-Schauder度理论,建立了系统非常稳态解的存在性定理.The nonconstant stationary solutions of a diffusive predator-prey system with hunting cooperative are investigated.With the help of Maximum principle and Harnack inequality,a priori estimate for the positive solutions of this system is given.Based on Poincaréinequality,the nonexistence of nonconstant stationary solutions is shown.Finally,the existence of nonconstant stationary solutions is established by using Leray-Schauder degree.

关 键 词：捕食者-食饵系统 协作捕食 非常值稳态解 LERAY-SCHAUDER度 

分 类 号：O29[理学—应用数学]