Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

Abstract

The oscillation of solutions of the second-order nonlinear dynamic equation $\left(r\right(t\left)\right(x^{\Delta }\left(t\right){)}^{\gamma }{)}^{\Delta }+p\left(t\right)\left(x^{\Delta }\right(t){)}^{\gamma }+f(t,x\left(g\right(t\left)\right))=0$, with damping on an arbitrary time scale $\mathbb{T}$, is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.