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Comparison and linearized oscillation theorems for a nonlinear partial difference equation

Published online by Cambridge University Press:  17 February 2009

B. G. Zhang  and
Jian-She Yu
B. G. Zhang
Affiliation:
Department of Mathematics, Ocean University of Qingdao, Qingdao 266003, P. R. China. E-mail: bgzhang@public.gd.sd.cn
Jian-She Yu
Affiliation:
Department of Applied Mathematics, Hunan University, Changsha, Hunan 410082, P. R. China
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Abstract

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Connections between a linear partial difference equation with constant coefficients and a nonlinear partial difference equation are established by means of a comparison theorem and a continuous dependence of parameters theorem. A linearized oscillation theorem is also established as an application.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 4 , April 2001 , pp. 552 - 560
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Agarwal, R. P., Difference Equations and Inequalities (Marcel Dekker, New York, 1992).Google Scholar
[2]Courant, R., Friedrichs, K. and Lewy, H., “On partial difference equations of mathematical physics”, IBM J. 11 (1967) 215–234.Google Scholar
[3]Gregor, J., “The multidimensional z-transform and its use in solution of partial difference equations”, Kybernetika Supplement 24 (1988) 1–40.Google Scholar
[4]Levy, H. and Lessaman, F., Finite Difference Equations (Dover Publications, New York, 1992).Google Scholar
[5]Zhang, B. G. and Liu, S. T., “Oscillation of partial difference equations”, PanAmerican Math. J. 5 (1995) 61–70.Google Scholar
[6]Zhang, B. G. and Liu, S. T., “Necessary and sufficient conditions for oscillations of partial difference equations”, Dynamic of Continuous, Discrete and Impulsive Systems 3 (1997) 89–96.Google Scholar
[7]Zhang, B. G. and Liu, S. T., “On the oscillation of two partial difference equations”, J. Math. Anal. Appl. 206 (1997) 480–492.Google Scholar
[8]Zhang, B. G., Liu, S. T. and Cheng, S. S., “Oscillation of a class of delay partial difference equations”, J. Difference Eq. Appl. 1 (1995) 215–226.Google Scholar
[9]Zhang, B. G. and Yu, J. S., “Linearized oscillation theorems for certain nonlinear delay partial difference equations”, Computers Math. Applic. 35 (1998) 111–116.Google Scholar