Acta Mathematicae Applicatae Sinica

, Volume 20, Issue 1, pp 101–114 | Cite as

Nonoscillation for a Second Order Linear Delay Differential Equation with Impulses

  • Yan-ling Tian
  • Pei-xuan Weng1
  • Jin-ji Yang
Original Papers

Abstract

A group of necessary and sufficient conditions for the nonoscillation of a second order linear delay equation with impulses
$$ {\left( {r{\left( t \right)}{u}\ifmmode{'}\else$'$\fi} \right)}^{\prime } = - p{\left( t \right)}u{\left( {t - r} \right)} $$
are obtained in this paper, where \( p{\left( t \right)} = {\sum\limits_{n = 1}^\infty {\alpha _{n} \delta {\left( {t - t_{n} } \right)},{\kern 1pt} \delta {\left( t \right)}} } \) is a Dirac δ−function, and for each n ∈ N, αn > 0, tn → ∞ as n → ∞. Furthermore, the boundedness of the solutions is also investigated if the equation is nonoscillatory. An example is given to illustrate the use of the main theorems.

Keywords

nonoscillation impulse linear delay differential equation boundedness 

2000 MR Subject Classification

34K10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Yan-ling Tian
    • 1
  • Pei-xuan Weng1
    • 1
  • Jin-ji Yang
    • 2
  1. 1.Department of MathematicsSouth China Normal UniversityGuangzhou 510631China
  2. 2.Department of Computer SciencesSouth China Normal UniversityGuangzhou 510631China

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