东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2007, Vol. 28 ›› Issue (9): 1358-1360+1364.DOI: -

• 论著 • 上一篇    下一篇

非线性随机移民扰动人口发展方程局部解的存在性

刘超;孙涛;段晓东;   

  1. 东北大学理学院;东北大学理学院;大连民族学院计算机学院 辽宁沈阳110004;辽宁沈阳110004;辽宁大连116600
  • 收稿日期:2013-06-24 修回日期:2013-06-24 出版日期:2007-09-15 发布日期:2013-06-24
  • 通讯作者: Liu, C.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(60573124)

Existence of local solutions to nonlinear evolutional population equations with random migration perturbation

Liu, Chao (1); Sun, Tao (1); Duan, Xiao-Dong (2)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) School of Computer, Dalian Nationalities University, Dalian 116600, China
  • Received:2013-06-24 Revised:2013-06-24 Online:2007-09-15 Published:2013-06-24
  • Contact: Liu, C.
  • About author:-
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摘要： 研究人口系统的数学模型通常没有考虑外界环境对系统的影响,随着社会经济的快速发展,人口流动日益频繁,因此随机移民扰动已经成为影响人口系统的一个重要因素.在假设随机的外界环境对人口迁移产生扰动的条件下,应用非线性泛函分析理论中的m增生算子理论与非线性半群理论,在A为m增生算子,B为凝聚紧算子的前提下,针对确定型与随机型两种情况研究了具有随机移民扰动的非线性人口发展方程,并获得了该类方程局部解的存在性定理.

关键词: 发展方程, m增生算子, 随机不动点, 凝聚映射, 随机扰动

Abstract: Generally the mathematical models for population system take no account of the influence of exterior conditions. However, the number of migrating people is increasing rapidly along with the socio-economic development, and the random migration becomes an important perturbative factor to population system. Assuming that the random exterior conditions perturb people's migration, the theories of m-accretive operator and nonlinear semigroup, as the terms included in the nonlinear functional analysis, are applied to deriving the nonlinear equations of evolutional population with random migration perturbation in either definite case or random case, where A represents the m-accretive operator and B the condensing map. Consequently, the theorems proving the existence of local solutions to those equations are obtained.

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