Oscillation Criteria for Nonlinear Second-order Damped Delay Dynamic Equations on Time Scales
In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59409", author = "Da-Xue Chen and Guang-Hui Liu", title = "Oscillation Criteria for Nonlinear Second-order Damped Delay Dynamic Equations on Time Scales", abstract = "In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.
", keywords = "Oscillation, damped delay dynamic equation, time scale.", volume = "4", number = "1", pages = "99-8", }