Dependence Of Population Size On Random Dispersal Rate

In this paper,we mainly study how the total number of single species depends on the random diffusion rate in inhomogeneous environment.The main research equation is the Logistic equationIn the theorem 2.4 of paper [17],The author discussed how the population depends on random diffusion rate in the case of ? =(0,1),where a in(0,1)and ? > 0.Inspired by the above conclusions,this paper mainly discusses whether the two conclusions in the theorem 2.4 of paper [17] can be analogized while ? =(0,1),We strictly use the upper and lower solutions,the Dominated convergence theorem and some other important theorems and lemmas to prove our conclusions.