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

Article Sidebar

PDF
Published: Sep 1, 1998
DOI: https://doi.org/10.5556/j.tkjm.29.1998.4274
Keywords:
Recurrence relation eventually positive solution

Main Article Content

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.

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 : $x_{n+1}-x_n+p_nx_{n-r}\le 0$.




Article Details

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
Issue
Vol. 29 No. 3 (1998)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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.