Scalar Delay Differential Equations on Semiaxes

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 2 in Nonoscillation Theory of Functional Differential Equations with Applications, 2012, pp 23-58 from Springer

Abstract: Abstract Chapter 2 deals with nonoscillation properties of scalar differential equations with positive coefficients and a finite number of delays. There are several monographs and a lot of papers on oscillation, however, there are not so many results on nonoscillation, especially in monographs on the oscillation theory. One of the aims of this chapter is to consider nonoscillation together with other relevant problems: differential inequalities, comparison results, solution estimations, sufficient conditions for positivity of solutions of the initial value problem, stability, slowly oscillating solutions. The second purpose is to derive some nonoscillation methods which will be used for other classes of functional differential equations. In particular, a solution representation formula is applied here, so the most important nonoscillation property is the positivity of the fundamental function of the considered equation. Other results of this chapter include explicit oscillation conditions and a discussion of the well-known constants 1 and 1/e which are usually used in oscillation and nonoscillation conditions, and of the case when the values of the computed parameter are between the two constants.

Keywords: Scalar Delay Differential Equation; Nonoscillation Conditions; Non-oscillatory Method; Nonoscillatory Solution; Oscillation Results (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3455-9_2

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