International Journal of Pure and Applied Mathematics ————————————————————————– Volume 72 No. 4 2011, 591-597 OSCILLATION CRITERIA FOR EVEN ORDER DYNAMIC EQUATIONS ON TIME–SCALES Said R. Grace 1 , Ravi P. Agarwal 2 § , Billˆ ur Kaymak¸ calan 3 1 Department of Engineering Mathematics Faculty of Engineering Cairo University Orman, Giza 12221, EGYPT 2 Department of Mathematics Texas A&M University-Kingsville Kingsville, TX 78363, USA 3 Department of Mathematics and Computer Science C¸ ankaya University Eski¸sehir Yolu, 29 km, Yukar´ y Yurt¸ cu, Ankara, TURKEY Abstract: Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form x Δ n (t)+ q(t)x(t)=0 are established. AMS Subject Classification: 34K11, 34C10, 39A11 Key Words: oscillation, nonoscillation, dynamic equation 1. Introduction This paper is concerned with the oscillatory behavior of all solutions of the even order dynamic equation x Δ n (t)+ q(t)x(t)=0 (1.1) on an arbitrary time-scale I T ⊆ IRwith sup I T= ∞, where q :I T → IR + = (0, ∞) is real-valued rd-continuous function. Received: November 18, 2011 c  2011 Academic Publications, Ltd. § Correspondence author