First-Order Linear Delay Impulsive Differential Equations
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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.
KeywordsImpulsive Delay Differential Equations Linear Delay Impulsive Diﬀerential Equations Nonoscillation Criteria Delay Distribution Nonoscillation Conditions
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