Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1457-1464.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 34K11
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