一类捕食-被捕食模型的正平衡解存在性  

Existence of Positive Solutions of a Predator-Prey Model

作　　者：吕明海[1] 侯立春[2] 

机构地区：[1]辽宁工程技术大学基础教学部,辽宁葫芦岛125105 [2]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《数学的实践与认识》2013年第24期107-112,共6页Mathematics in Practice and Theory

基　　金：教育部高校博士学科点专项科研基金(20102121110002);辽宁省高等学校科研项目(L2012105);辽宁工程技术大学研究生科研立项资助(Y201201003)

摘　　要：针对自然界中捕食者染病的现象,建立了捕食者染病的捕食-被捕食模型,研究了捕食者为躲避疾病进行扩散,并且具有HollingⅡ功能性反应函数和齐次Neumann边界条件的问题,利用Harnack不等式和最大值原理给出反应扩散问题的正平衡解的先验估计,并利用拓扑度理论证明该问题的非常数正平衡解的存在性.讨论了对应平衡态问题的非常数正平衡解存在性。In the view of the phenomenon that the predator is sick,a predator-prey model with an epidemic in the predator is considered. A system with diffnsion and a Holling type II function under the homogeneous Neumann boundary condition is studied,the existence for a steady state of the corresponding steady state problem is discussed.First,discuss the condition of the development of the field and introduce the theorems; Secondly, a prior estimates of the positive steady states of the reaction-diffusion system is given by the Harnack inequation and maximum principle;Finally, the existence of non-constant positive steady state is obtained by using the topological degree.

关 键 词：捕食一被捕食模型 HollingII 交错扩散 拓扑度 

分 类 号：O175[理学—数学]