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 (r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t))γ+f(t,x(g(t)))=0, with damping on an arbitrary time scale 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.