Abstract and Applied Analysis
Volume 2011 (2011), Article ID 637142, 14 pages
http://dx.doi.org/10.1155/2011/637142
Research Article

On Nonoscillation of Advanced Differential Equations with Several Terms

1Department of Mathematics, Ben-Gurion University of Negev, Beer-Sheva 84105, Israel
2Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4

Received 16 December 2010; Accepted 27 January 2011

Academic Editor: Josef Diblík

Copyright © 2011 L. Berezansky and E. Braverman. 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

Existence of positive solutions for advanced equations with several terms ∑ ̇ 𝑥 ( 𝑡 ) + 𝑚 𝑘 = 1 𝑎 𝑘 ( 𝑡 ) 𝑥 ( ℎ 𝑘 ( 𝑡 ) ) = 0 , ℎ 𝑘 ( 𝑡 ) ≥ 𝑡 is investigated in the following three cases: (a) all coefficients 𝑎 𝑘 are positive; (b) all coefficients 𝑎 𝑘 are negative; (c) there is an equal number of positive and negative coefficients. Results on asymptotics of nonoscillatory solutions are also presented.