| Recently,the study of predator-prey model by biologist is more practical than before,and it has three directions:1.The influence factors have become more.2.The dimension is becoming more and more.3.Put practical prob-lem into detailed study. The study of predator-prey model can direct us to development and utilization reasonably,and it has an influence on sustainable development problem in direct. And it is significant for the study of biodiver-sity and Biological reserve construction[1-5]. In this paper,we investigate the positive stationary solution to a diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemesWhere,Ω(?)RN is a bounded domain with a smooth boundary.γ is the unit normal vector of (?)Ω, outside,the parameters λ and a1, b, b2, c1, C2,k1,k2 are positive numbers, u and v are the respective populations of prey and predator.We use degree theory and fixed point theory mainly,combining proof of contradiction to prove that the existence of the stationary positive solutions to problem (M) varys correspondingly when parameter A takes different values on axially of real.The thesis is divided into three chapters,the main contents are as follows:In chapter one,we introduce the background of population ecology and the development of predator-prey model. Then we give the presentation of the main issues of this article,and then give some basic theory of partial differential equation.In the second chapter,we discuss the results of problem (2.1) under two conditions respectively. At first,a lemma about the positive solution’s bound-edness of problem (2.1) is given. And then combining lemma proved before,we prove the existence of positive solution of (2.1) through using degree theory and fixed point theory. At last,the influence of exerted A on (2.1) is discussed using existence theory proved above.In the third chapter,the innovation of this article will be mentioned,and so as further questions of which have not been learned. |
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