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

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.