A new oscillation criterion for two-dimensional dynamic systems on time scales

Main Article Content

Jia Baoguo

Abstract

Consider the linear dynamic system on time scales
\begin{equation}
u^\Delta=pv, \quad\quad v^\Delta=-qu^\sigma
\end{equation}
where $p>0$ and $q$ are rd-continuous functions on a time scale $\mathbb T$ such that $\sup\mathbb T=\infty$. When $p(t)$ is allowed to take on negative values, we establish an oscillation criterion for system (0.1). Our result improves a main result of Fu and Lin [S. C. Fu and M. L. Lin, Oscillation and nonoscillation criteria for linear dynamic systems on time scales, Computers and Mathematics with Applications, 59(2010), 2552-2565].

Article Details

How to Cite
Baoguo, J. (2011). A new oscillation criterion for two-dimensional dynamic systems on time scales. Tamkang Journal of Mathematics, 42(2), 237–244. https://doi.org/10.5556/j.tkjm.42.2011.656
Section
Papers

References

Shengchen Fu, Mingli Lin, Oscillation and nonoscillation criteria for linear dynamic equations on time scales, Computers and Mathematics with Applications, 59(2010), 2552-2565.

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M. Bohner and A. Peterson, Dynamic Equation on Time Scales: An Introduction with Applications, Birkh"{a}user, Boston, 2001.

Lynn Erbe, Oscillation criteria for second order linear equations on a time scale, Canad. Appl. Math. Quart., 9 (2001) 346--375.

Jia Baoguo, Lynn Erbe and Allan Peterson, A Wong-type oscillation theorem for second order linear dynamic equations on time scales, J. Difference Equs. Appl., 16(2010), 15-36.

W. A. Coppel, Disconjugacy, Lecture Notes In Mathematics, Springer-Verlag, No. 220,1971, 17-18.