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First-Order Linear Delay Impulsive Differential Equations

  • Ravi P. Agarwal
  • Leonid Berezansky
  • Elena Braverman
  • Alexander Domoshnitsky
Chapter
  • 841 Downloads

Abstract

Chapter 12 presents nonoscillation results for first-order linear impulsive differential equations with both concentrated and distributed delays. The main result of this chapter is that oscillation (nonoscillation) of the impulsive delay differential equation is equivalent to oscillation (nonoscillation) of a certain differential equation without impulses which can be constructed explicitly from an impulsive equation. Thus, oscillation problems (in particular, oscillation and nonoscillation criteria) for an impulsive equation can be reduced to the similar problem for a certain nonimpulsive equation. In this chapter, nonoscillation criteria, comparison theorems and explicit nonoscillation conditions are presented.

Keywords

Impulsive Delay Differential Equations Linear Delay Impulsive Differential Equations Nonoscillation Criteria Delay Distribution Nonoscillation Conditions 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
  • Leonid Berezansky
    • 2
  • Elena Braverman
    • 3
  • Alexander Domoshnitsky
    • 4
  1. 1.Department of MathematicsTexas A&M University—KingsvilleKingsvilleUSA
  2. 2.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  3. 3.Department of MathematicsUniversity of CalgaryCalgaryCanada
  4. 4.Department of Computer Sciences and MathematicsAriel University Center of SamariaArielIsrael

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