Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 98423, 13 pages
Research Article

Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments

R. S. Dahiya1 and A. Zafer2

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.


We derive oscillation criteria for general-type neutral differential equations [x(t)+αx(tτ) +βx(t+τ)](n)=δabx(ts)dsq1(t,s)+δcdx(t+s)dsq2(t,s)=0, tt0, where t00, δ=±1, τ>0, b>a0, d>c0, α and β are real numbers, the functions q1(t,s):[t0,)×[a,b] and q2(t,s):[t0,)×[c,d] 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.