Second-Order Delay 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 7 in Nonoscillation Theory of Functional Differential Equations with Applications, 2012, pp 171-192 from Springer

Abstract: Abstract Equations of the second order are popular due to their numerous applications. For equations of the second order with several delays and not including explicitly the first derivative, Chap. 7 presents nonoscillation criteria in the terms of the fundamental function of the equation and the generalized Riccati inequality. In addition, the chapter includes comparison results, explicit nonoscillation and oscillation conditions, the result that the equation is oscillatory if and only if it has a slowly oscillating solution, and explicit nonoscillation conditions which are obtained by substituting specific solutions of the generalized Riccati inequality. Sufficient conditions for positivity of a solution of the initial value problem are also presented in Chap. 7.

Keywords: Second-order Delay Differential Equations; Nonoscillation Criteria; Nonoscillation Conditions; Non-oscillatory Property; Discontinuous Parameters (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3455-9_7

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