First-Order Linear Delay Impulsive Differential Equations

Ravi P. Agarwal, Leonid Berezansky, Elena Braverman and Alexander Domoshnitsky
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Ravi P. Agarwal: Texas A&M University—Kingsville, Department of Mathematics
Leonid Berezansky: Ben-Gurion University of the Negev, Department of Mathematics
Elena Braverman: University of Calgary, Department of Mathematics
Alexander Domoshnitsky: Ariel University Center of Samaria, Department of Computer Sciences and Mathematics

Chapter Chapter 12 in Nonoscillation Theory of Functional Differential Equations with Applications, 2012, pp 285-300 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-3455-9_12

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DOI: 10.1007/978-1-4614-3455-9_12

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