Rocky Mountain Journal of Mathematics

Existence of eventually positive solutions of higher order impulsive delay differential equations

Shao Yuan Huang and Sui Sun Cheng

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Abstract

A search of the literature reveals only a few studies on the necessary as well as sufficient conditions for the existence of eventually positive and/or monotone solutions of higher order impulsive differential equations that also allow delays. To fill this gap, we study a general class of higher order impulsive delay differential equations and establish necessary and/or sufficient conditions for the existence of eventually positive and monotone solutions. Our results are sharp in the sense that, in special cases, they are necessary and sufficient. Illustrative examples are included.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 1 (2015), 237-271.

Dates
First available in Project Euclid: 7 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1428412779

Digital Object Identifier
doi:10.1216/RMJ-2015-45-1-237

Mathematical Reviews number (MathSciNet)
MR3334210

Zentralblatt MATH identifier
1325.34090

Subjects
Primary: 34K11: Oscillation theory 34K45: Equations with impulses

Keywords
Impulsive differential equation delay positive solution comparison theorem oscillation criteria

Citation

Huang, Shao Yuan; Cheng, Sui Sun. Existence of eventually positive solutions of higher order impulsive delay differential equations. Rocky Mountain J. Math. 45 (2015), no. 1, 237--271. doi:10.1216/RMJ-2015-45-1-237. https://projecteuclid.org/euclid.rmjm/1428412779


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