Abstract
Oscillation Behavior of Second Order Nonlinear Dynamic Equation with Damping on Time Scales
Highlights
The calculus theory of time scales was introduced by Hilger [1] in order to unify, extend and generalize ideas from discrete calculus, quantum calculus and continuous calculus to arbitrary time scales calculus
We are concerned with the oscillation behavior of all solutions of the second order nonlinear dynamic equation with damping on a time sceles T which is unbounded above (r(t)(x∆(t))α)∆ − p(t)(x∆(t))α + q(t)f (x(t)) = 0, (1)
Much interest has focused on obtaining sufficient conditions for the oscillation of solutions of different classes of dynamic equations on time scales, and we refer the reader to the papers [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
Summary
The calculus theory of time scales was introduced by Hilger [1] in order to unify, extend and generalize ideas from discrete calculus, quantum calculus and continuous calculus to arbitrary time scales calculus. We are concerned with the oscillation behavior of all solutions of the second order nonlinear dynamic equation with damping on a time sceles T which is unbounded above (r(t)(x∆(t))α)∆ − p(t)(x∆(t))α + q(t)f (x(t)) = 0,. Oscillation behavior of second order nonlinear dynamic equation with damping on time scales 79 where t ∈ T, t t0 > 0. Much interest has focused on obtaining sufficient conditions for the oscillation of solutions of different classes of dynamic equations on time scales, and we refer the reader to the papers [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Erbe et al [15] considered the second-order nonlinear damped dynamic equation (r(t)(x∆(t))γ )∆ + p(t)(x∆σ(t))γ + q(t)f (x(τ (t))) = 0, and obtained some oscillation criteria.
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