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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 818732, 11 pages
Research Article

On Eventually Positive Solutions of Quasilinear Second-Order Neutral Differential Equations

Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic

Received 17 February 2014; Accepted 16 April 2014; Published 13 May 2014

Academic Editor: Samir Saker

Copyright © 2014 Simona Fišnarová and Robert Mařík. 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.


We study the second-order neutral delay differential equation , where , and . Based on the conversion into a certain first-order delay differential equation we provide sufficient conditions for nonexistence of eventually positive solutions of two different types. We cover both cases of convergent and divergent integral . A suitable combination of our results yields new oscillation criteria for this equation. Examples are shown to exhibit that our results improve related results published recently by several authors. The results are new even in the linear case.