一类非线性种群发展方程非局部柯西问题随机周期解的存在性

The Existence of Random Periodic Solutions for a Class Non-local Cauchy Problem of Nonlinear Population Evolution Equation

研究如下形式具有随机周期移民扰动的非线性种群发展方程的非局部柯西问题,{(p(r,t))/(t)+(p(r,t))/(r)=-μ(r)p(r,t)+f(t,p(r,t)),0<r<rm,t0p(r,0)=p0(r)+g(p(r,t0)),T>t0>0 p(0,t)=β(t)integral from n=r1 to r2 k(r)h(r)p(r,t)dr这里,其他地区的种群迁入项f以及非局部条件项g为紧算子,且f是时间变量t的周期为T的周期函数.利用Shesfer不动点定理,可以证明上述柯西问题随机周期积分解的存在性.这篇论文的结果推广了前人的工作.

In this paper, we investigate the following non-local Cauchy problem of nonlinear population evolution equation with random periodic migration perturbation,{δp（r,t）/δt＋δp（r,t）/δr=-μ（r）p（r,t）＋f（t,p（r,t））,0〈r〈rm,t≥0,p（r,0）=p0（r）＋g（p（r,t0））,T〉t0〉0 p（0,t）=β（t）∫^r2 r1（k（r）h（r）p（r,t）dr Here, we let the migration item f and the non-local condition item g as compact operator, and the function f is a periodic function of time veriable t with period T. Using the Shesfer fixed point theorem, the existence of random periodic solution for the above Cauchy problem was proved. Our results generalize the former researches.