Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales

This paper is concerned with nth-order nonlinear dynamic equations on time scales of the form (r(t)Φγ(xΔn−1(t)))Δ+∑i=0kqi(t)Φαi(x(δi(t)))=0with n ≥ 2. By discussing the signs of i  th-order derivatives of eventually positive solutions for i=1,…,n−1,i=1,…,n−1, and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results extend many existing results in the literature.