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Abstract:We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t) - a(t)x(tau(1)(t)))(Delta) = p(t)f(1)(y(t)), y(Delta)(t) = -q(t)f(2)(x(tau(2)(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 a(n) to be a positive real sequence. Some examples are given to illustrate the main results.

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