Abstract
We are concerned with the interval oscillation of general type of forced second-order nonlinear dynamic equation with oscillatory potential of the formrtg1xt,xΔtΔ+p(t)g2(x(t),xΔ(t))xΔ(t)+q(t)f(x(τ(t)))=e(t), on a time scaleT. We will use a unified approach on time scales and employ the Riccati technique to establish some oscillation criteria for this type of equations. Our results are more general and extend the oscillation criteria of Erbe et al. (2010). Also our results unify the oscillation of the forced second-order nonlinear delay differential equation and the forced second-order nonlinear delay difference equation. Finally, we give some examples to illustrate our results.
Highlights
We are concerned with the interval oscillation of general type of forced second-order nonlinear dynamic equation with oscillatory potential of the form (r(t)g1(x(t), xΔ(t)))Δ + p(t)g2(x(t), xΔ(t))xΔ(t) + q(t)f(x(τ(t))) = e(t), on a time scale T
We will use a unified approach on time scales and employ the Riccati technique to establish some oscillation criteria for this type of equations
The theory of time scales, which has recently received a lot of attention, was originally introduced by Hilger in his Ph.D. thesis [1], in order to unify, extend, and generalize ideas from discrete calculus, quantum calculus, and continuous calculus to arbitrary time scale calculus
Summary
The theory of time scales, which has recently received a lot of attention, was originally introduced by Hilger in his Ph.D. thesis [1], in order to unify, extend, and generalize ideas from discrete calculus, quantum calculus, and continuous calculus to arbitrary time scale calculus. We are concerned with the interval oscillation of general type of forced second-order nonlinear dynamic equation with oscillatory potential of the form (r(t)g1(x(t), xΔ(t)))Δ + p(t)g2(x(t), xΔ(t))xΔ(t) + q(t)f(x(τ(t))) = e(t), on a time scale T. We will use a unified approach on time scales and employ the Riccati technique to establish some oscillation criteria for this type of equations. We are concerned with the interval oscillation of the second-order nonlinear dynamic equation: (r (t) g1 (x (t) , xΔ (t)))Δ
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
