Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 98423, 13 pages
doi:10.1155/2007/98423
Research Article
Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments
1Department of Mathematics, Iowa State University, Ames 50010, IA, USA
2Department of Mathematics, Middle East Technical University, Ankara 06531, Turkey
Received 19 October 2006; Accepted 15 May 2007
Academic Editor: Ondrej Dosly
Copyright © 2007 R. S. Dahiya and A. Zafer. 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
We derive oscillation criteria for general-type neutral differential equations
[x(t)+αx(t−τ) +βx(t+τ)](n)=δ∫abx(t−s)dsq1(t,s)+δ∫cdx(t+s)dsq2(t,s)=0, t≥t0, where t0≥0, δ=±1, τ>0, b>a≥0, d>c≥0, α and β are real numbers, the functions q1(t,s):[t0,∞)×[a,b]→ℝ and q2(t,s):[t0,∞)×[c,d]→ℝ are nondecreasing in s for each fixed t, and τ is periodic and continuous with respect to t for each fixed s. In certain special cases, the results obtained generalize and improve some existing ones in the literature.