QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (III): FORCED OSCILLATIONS OF PARABOLIC TYPE PARTIAL DIFFERENCE EQUATIONS

Authors

  • SUI SUN CHENG Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan, 300043 R.O.C.
  • SHENG-LI XIE Department of Mathematics, Jinzhou Teacher's College, Hubei, China, 434100.
  • BING-GEN ZHANG Department of Mathematics, Ocean University of Qingdao, Qingdao, China, 266003.

DOI:

https://doi.org/10.5556/j.tkjm.26.1995.4395

Keywords:

Partial difference equations, oscillatoin criteria

Abstract

Parabolic type partial difference equations with a forcing term is stud- ied in this paper. By means of three averaging techniques, the problem of oscillation of these equations is reduced to that of recurrence relations in one variable. Avariety of oscillation criteria is given for these recurrence relations which in turn yield oscillation criteria for the partial difference equations.

References

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

S. S. Cheng and B. G. Zhang, "Qualitiative theory of partial difference equations (I): Oscillation of nonlinear partial difference equations," Tamkang J. Math., 25 (1994), 279-288.

S. S. Cheng, S. L. Xie and B. G. Zhang, "Qualitative theory of partial difference equations (II): Oscillation criteria for direct control systems in several variables," Tamkang J. Math., Vol.25, no.I, 1995.

S. S. Cheng, "A discrete analogue of the inequality of Lyapunov," Hokkaido Math. J., 12 (1983), 105-112.

S. S. Cheng, "Discrete quadratic Wirtinger's inequalities," Linear Alg. Appl., 94 (1987), 57-73.

N. Yoshida, "Oscillation of nonlinear parabolic equations with functional arguments," Hiroshima Math. J., 16 (1986), 305-314.

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Published

1995-06-01

How to Cite

CHENG, S. S., XIE, S.-L., & ZHANG, B.-G. (1995). QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (III): FORCED OSCILLATIONS OF PARABOLIC TYPE PARTIAL DIFFERENCE EQUATIONS. Tamkang Journal of Mathematics, 26(2), 177–192. https://doi.org/10.5556/j.tkjm.26.1995.4395

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