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《Acta Analysis Functionalis Applicata》 2008-01
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The Existence of Random Periodic Solutions for a Class Non-local Cauchy Problem of Nonlinear Population Evolution Equation

LIU Xiao-jing, WU Kai-su, XUE Ya-pingDepartment of Mathematics and Information Science, Beijing University of Chemical Technology, Beijing 100029, China  
In this paper, we investigate the following non-local Cauchy problem of nonlinear population evolution equation with random periodic migration perturbation,{(p(r,t))/(t)+(p(r,t))/(r)=-μ(r)p(r,t)+f(t,p(r,t)),0rrm,t0p(r,0)=p0(r)+g(p(r,t0)),Tt00 p(0,t)=β(t)integral from n=r1 to r2 k(r)h(r)p(r,t)dr, t≥0.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.
【Fund】: 北京化工大学青年科学基金资助(QN0622)
【CateGory Index】: O175
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