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

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

Recommended by Ondrej Dosly

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.