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

摘要

In this paper, by using the Riccati transformation technique, chain rule and inequalityAλ-λABλ-1+(λ-1)Bλ⩾0,λ>1,where A and B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation(p(t)(xΔ(t))γ)Δ+q(t)xγ(t)=0,t∈[a,b]on time scales, where γ>1 is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results.