Abstract and Applied Analysis
Volume 2011 (2011), Article ID 730128, 10 pages
http://dx.doi.org/10.1155/2011/730128
Research Article

Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

J. Džurina and R. Komariková

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

Received 2 September 2010; Accepted 3 November 2010

Academic Editor: Yuri Rogovchenko

Copyright © 2011 J. Džurina and R. Komariková. 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 aim of this paper is to study properties of the third-order delay trinomial differential equation ( ( 1 / 𝑟 ( 𝑡 ) ) 𝑦 ″ ( 𝑡 ) ) ′ + 𝑝 ( 𝑡 ) 𝑦 ′ ( 𝑡 ) + 𝑞 ( 𝑡 ) 𝑦 ( 𝜎 ( 𝑡 ) ) = 0 , by transforming this equation onto the second-/third-order binomial differential equation. Using suitable comparison theorems, we establish new results on asymptotic behavior of solutions of the studied equations. Obtained criteria improve and generalize earlier ones.