OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES

Abstract

By means of generalized Riccati transformation techniques and generalized exponential functions, some oscillation criteria are given for the nonlinear dynamic equation ( p ( t ) x Δ ( t ) ) Δ + q ( t ) ( f o x σ ) = 0 on time scales. The results are also applied to linear and nonlinear dynamic equations with damping, and some sufficient conditions are obtained for the oscillation of all solutions.