## Rocky Mountain Journal of Mathematics

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

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

Shao Yuan Huang and Sui Sun Cheng

#### 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