Oscillation criteria for two-dimensional dynamic systems on time scales

Authors:
Youjun Xu;Zhiting Xu
Affiliations:
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, PR China;School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We establish some oscillation criteria for the two-dimensional dynamic system {x^@D(t)=b(t)g[y^@s(t)],y^@D(t)=-a(t)f[x(t)], on a time scale T. Our results not only unify the oscillation of two-dimensional differential systems and difference systems, but include the oscillation results for differential systems and provide new oscillation criteria for difference systems. Several examples are considered to illustrate the main results.