Oscillation of Two-Dimensional Neutral Delay Dynamic Systems

Abstract

We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t)=0 improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case where f(u)=u. Also, as a special case when 𝕋=ℝ, our results do not require an to be a positive real sequence. Some examples are given to illustrate the main results.