Numerical verification of certain oscillation result on time scales

Abstract

We first investigate several examples of second order nonlinear dynamic equation (a(xδ)α)δ(t)+q(t) xβ(t)=0 which can also be rewritten in the form of two-dimensional dynamic system xδ(t)=b(t)g[y σ(t)]and yδ(t) = -c(t)f[x(t)] where α and ß are ratios of positive odd integers, o and q are real-valued, positive and rd-continuous functions on a time scale T C R with sup T = oo. Under oscillation criteria, some equations are then selected. Exploring the numerical solution of corresponding dynamic system individually on different time scales not only visualizes the oscillating motion as theoretically expected but also reveals other interesting behavior patterns. This study finally suggests that a time domain also plays an important role on the boundedness of oscillatory solution. © Dynamic Publishers Inc.