Some Oscillation Criteria for Higher-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

Abstract

New oscillation criteria are established for higher-order Emdn-Fowler dynamic equation q ( v ) x β ( δ ( v ) ) + ( r ( v ) ( z Δ n - 1 ( v ) ) α ) Δ = 0 $ q(v)x^{\beta } (\delta (v)) + (r(v)(z^{{\Delta ^{{n - 1}} }} (v))^{\alpha } )^{\Delta } = 0 $ on time scales, z ( v ) : = p ( v ) x ( τ ( v ) ) + x ( v ) $ z(v): = p(v)x(\tau (v)) + x(v) $ Our results extend and supplement those reported in literatures in the sense that we study a more generalized neutral delay equation and do not require r Δ ( v ) ≥ 0 $ r^{\Delta } (v) \ge 0 $ and the commutativity of the jump and delay operators.