QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (I): OSCILLATION OF NONLINEAR PARTIAL DIFFERENCE EQUATIONS

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Published: Sep 1, 1994
DOI: https://doi.org/10.5556/j.tkjm.25.1994.4455
Keywords:
Nonlinear partial difference equation oscillation

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SUI SUN CHENG
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan, 30043.
BING-GEN ZHANG
Department of Applied Mathematics, Ocean University of Qingdao, Qingdao, China.

Abstract




This paper is concerned with a class of nonlinear partial difference equations with delay. By means of an averaging technique, and several oscillation criteria for ordinary recurrence relations, we are able to establish several oscillation criteria for the partial difference equations.




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How to Cite
CHENG, S. S., & ZHANG, B.-G. (1994). QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (I): OSCILLATION OF NONLINEAR PARTIAL DIFFERENCE EQUATIONS. Tamkang Journal of Mathematics, 25(3), 279–288. https://doi.org/10.5556/j.tkjm.25.1994.4455
Issue
Vol. 25 No. 3 (1994)
Section
Papers
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References

D. D. Bainov and D. P. Mishev, "Oscillation Theory for Neutral Differential Equations with Delay," Adam Hilger, Bristol, 1991.

I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1991.

C. Qian and J. Yan, "Existence and comparison results of positive solutions of difference equations," Funkcialaj Ekvacioj, 35(1992), 581-595.

B. S. Lalli and B. G. Zhang, "Oscillation and comparison theorems for certain neutral difference equations," J. Austral. Math. Soc., Ser. B, 34(1992), 245-256.

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.

L. H. Erbe and B. G. Zhang, "Oscillation of discrete analogues of delay equations," Differential and Integral Eq., 2(1989), 300-309.

G. S. Ladde, V. Lakshmikantham and B. G. Zhang, Oscillation theory of differential equations with deviating arguments, Marcel Dekker, New York, 1987.

S. S. Cheng and S. S. Lin, "Existence and uniqueness theorems for nonlinear difference boundary value problems," Utilitas Math., 39(1991), 167-i 86.

S. S. Cheng and R. F. Lu, "Discrete Wirtinger's inequalities and conditions for partial difference equations," Fasciculi Math., 23(1991), 9-24.

S. S. Cheng, L. Y. Hsieh and Z. T. Chao, "Discrete Ly'apunov inequality conditions for partial difference equations," Hokkaido Math. J., 19(1990), 229-239.