摘要：In this paper, we investigate the oscillation of the following higher order delay dynamic equation: { a n ( t ) [ ( a n − 1 ( t ) ( ⋯ ( a 1 ( t ) x Δ ( t ) ) Δ ⋯ ) Δ ) Δ ] α } Δ + g ( t , x ( τ ( t ) ) ) = 0 on any time scale T with sup T = ∞ . Here n ≥ 2 , a k ( t ) ∈ C rd ( T , ( 0 , ∞ ) ) ( 1 ≤ k ≤ n ), τ : T → T is an increasing differentiable function with τ ( t ) ≤ t and lim t → ∞ τ ( t ) = ∞ , g ∈ C ( T × R , R ) with g ( t , x ) / x β ≥ q ( t ) for some q ( t ) ∈ C rd ( T , ( 0 , ∞ ) ) when x ≠ 0 , and α ≥ 1 , β ≥ 1 are two quotients of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero. MSC:34K11, 34N05, 39A10.
