数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1035-1052.doi: 10.1016/S0252-9602(12)60077-0

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CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER#br# CURVES

K.G. Dishlieva   

  1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, 1756, Bulgaria
  • 收稿日期:2010-07-26 出版日期:2012-05-20 发布日期:2012-05-20

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER

K.G. Dishlieva   

  1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, 1756, Bulgaria
  • Received:2010-07-26 Online:2012-05-20 Published:2012-05-20

摘要:

The basic objects of investigation in this article are nonlinear impulsive dif-ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf-ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.

关键词: Impulsive differential equations, initial condition, barrier curves, continuous dependence, population dynamics

Abstract:

The basic objects of investigation in this article are nonlinear impulsive dif-ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf-ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.

Key words: Impulsive differential equations, initial condition, barrier curves, continuous dependence, population dynamics

中图分类号: 

  • 34A37