Oscillation criteria of second order half linear delay dynamic equations on time scales

Abstract

© 2017, Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg. In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation r(t)g(xΔ(t)))Δ+p(t)f(x(τ(t)))=0, on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=ℝ, difference equations when T=ℕ but can be applied on different types of time scales such as when T=qℕfor q > 1 and also improve most previous results. Finally, we give some examples to illustrate our main results.