ELEMENTARY OSCILLATION CRITERIA FOR A THREE TERM RECURRENCE RELATION WITH OSCILLATORY COEFFICIENT SEQUENCE

Authors

  • GUANG ZHANG Department of Mathematics, Datang Advanced College, Datong, Shanxi 037008, ·P. R. China.
  • SUI-SUN CHENG Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R. 0 . C.

DOI:

https://doi.org/10.5556/j.tkjm.29.1998.4274

Keywords:

Recurrence relation, eventually positive solution

Abstract

Qualitative properties of recurrence relations with coefficients taking on both positive and negative values are difficult to obtain since mathematical tools are scarce. In this note we start from scratch and obtain a number of oscillation criteria for one such relation : $x_{n+1}-x_n+p_nx_{n-r}\le 0$.

References

I. Gyori and G. Ladas , "Oscillation theory of delay differential equations," Oxford Mathe­matical Monographs, Clarendon Press, Oxford, 1991.

J. S. Yu, B. G. Zhang and X. Z. Qian, "Oscillations of delay difference equations with oscillating coefficients," J. Math. Anal. Appl., 177(1993), 432-444.

C. J. Tian, S. L. Xie and S. S. Cheng, "Measures for oscillatory sequences," Computers Math. Appl., to appear.

G. Ladas, L. Pakula and Z. Wang, "Necessary and sufficient conditions for the oscillation of difference equations," Pan Amer. Math. J., 2(1)(1992), 17-26.

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Published

1998-09-01

How to Cite

ZHANG, G., & CHENG, S.-S. (1998). ELEMENTARY OSCILLATION CRITERIA FOR A THREE TERM RECURRENCE RELATION WITH OSCILLATORY COEFFICIENT SEQUENCE. Tamkang Journal of Mathematics, 29(3), 227-232. https://doi.org/10.5556/j.tkjm.29.1998.4274

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Papers