Advances in Difference Equations
Volume 2010 (2010), Article ID 160761, 12 pages
doi:10.1155/2010/160761
Research Article

Comparison Theorems for the Third-Order Delay Trinomial Differential Equations

B. Baculíková and J. Džurina

Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia

Received 11 August 2010; Accepted 1 November 2010

Academic Editor: E. Thandapani

Copyright © 2010 B. Baculíková and J. Džurina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objective of this paper is to study the asymptotic properties of third-order delay trinomial differential equation 𝑦 ( 𝑡 ) + 𝑝 ( 𝑡 ) 𝑦 ( 𝑡 ) + 𝑔 ( 𝑡 ) 𝑦 ( 𝜏 ( 𝑡 ) ) = 0 . Employing new comparison theorems, we can deduce the oscillatory and asymptotic behavior of the above-mentioned equation from the oscillation of a couple of the first-order differential equations. Obtained comparison principles essentially simplify the examination of the studied equations.