数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1457-1464.

• 论文 • 上一篇    下一篇

有界时滞非线性随机微分方程解的振动性和非振性

汪红初1|胡适耕2|朱全新3
  

  1. 1.华南师范大学数学科学学院 广州 510631|2.华中科技大学数学系 武汉 430074|3.宁波大学理学院 浙江 宁波 315211
  • 收稿日期:2008-11-22 修回日期:2009-12-06 出版日期:2010-12-25 发布日期:2010-12-25
  • 基金资助:

    国家自然科学基金(10826095, 10801056)资助

Non-oscillation and Oscillation |in Solutions of Nonlinear Stochastic Differential Equations with Bounded Delay

 WANG hong-Chu1, HU Shi-Geng2, ZHU Quan-Xin3   

  1. 1.School of Mathematics Science, South China Normal University, Guangzhou 510631|2.Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074|3.Department of Mathematics, Ningbo University, Zhejiang Ningbo 315211
  • Received:2008-11-22 Revised:2009-12-06 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    国家自然科学基金(10826095, 10801056)资助

摘要:

研究了一类非线性随机时滞微分方程解的振动性和非振性,其中设定时滞可变且有界. 依据该方程漂移项和扩散项的性质, 证明了通过选定适当
的初值, 方程依概率存在正解; 同时, 给出了方程解几乎必然振动的一个充分条件.

 

关键词: 非线性, 非振性, 振动性, 布朗运动

Abstract:

This paper studies non-oscillation and oscillation in solutions of a nonlinear stochastic delay differential equation, in which the delay is time
varying and  bounded. Depending on the properties of the drift and the diffusion of the equation, positive solutions may exist with positive probability for suitable selected initial process, and a sufficient condition for the almost sure oscillation of the solutions is also established.

Key words: Nonlinear, Non-oscillation, Oscillation, Brownian motion

中图分类号: 

  • 34K11