Abstract
In this paper, we consider the oscillation behavior of the following second-order nonlinear dynamic equation. λ(s)Ψ1φΔ(s)y(φ(s))ΔΔ+η(s)Φ(y(τ(s)))=0,s∈[s0,∞)T. By employing generalized Riccati transformation and inequality scaling technique, we establish some oscillation criteria.
Highlights
The past decade has witnessed the tremendous development of time scale theory in many fields such as inequality and dynamic equation, which was established by Hilger [1]
We focus on the following second-order nonlinear dynamic equation: λ(s)Ψ
We explore a more general second-order nonlinear dynamic equation
Summary
The past decade has witnessed the tremendous development of time scale theory in many fields such as inequality and dynamic equation, which was established by Hilger [1]in 1988. Abstract: In this paper, we consider the oscillation behavior of the following second-order nonlinear dynamic equation. A great number of researches [10,11,12,13,14,15,16,17,18,19,20,21,22] have been done to explore the sufficient conditions which ensure every solution is oscillation in second-order dynamic equations on time scales. In 2008 and 2004, the authors investigated the following equations in [11,12], respectively.
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