Jozef Dzurina, Renata Kotorova, Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University, B. Nemcovej 32, 042 00 Kosice, Slovakia, e-mails: jozef.dzurina@tuke.sk, renata.kotorova@tuke.sk
Abstract: In this paper we study asymptotic properties of the third order trinomial delay differential equation
y"'(t)-p(t)y'(t)+g(t)y(\tau(t))= 0\tag{$*$}
by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.
Keywords: comparison theorem, property (A), canonical operator
Classification (MSC 2000): 34C10
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