Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales

Abstract

By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form $(r(t)x^{\mathrm{\Delta }}(t){)}^{\mathrm{\Delta }}+p(t)x^{\mathrm{\Delta }\sigma }(t)+q(t)(x^{\sigma }(t){)}^{\alpha }=F(t,x^{\sigma }(t))$ on a time scale $𝕋$ which is unbounded, where $\alpha$ is a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.