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A classification scheme for nonoscilatory solutions of a higher order neutral nonlinear difference equation

Part of: Difference equations Difference and functional equations

Published online by Cambridge University Press:  09 April 2009

Li Wan-Tong ,
Sui Sun Cheng  and
Guang Zhang
Li Wan-Tong
Affiliation:
Institute of Mathematics Gansu University of Technology Lanzhou, Gansu 730050 P. R., China
Sui Sun Cheng
Affiliation:
Department of Mathematics Tsing Hua University Hsinchu, Taiwan 30043 R. O. C.
Guang Zhang
Affiliation:
Department of Mathematics Datong Advanced CollegeDatong, Shanxi 037008 P. R., China
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Abstract

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Nonoscillatory solutions of a nonlinear neutral type higher order difference equations are classified by means of their asymptotic behaviors. Existence criteria are then provided for justification of such classficiation.

Keywords

Nolinear netural difference equationnonoscillatory solutionsuperlinear functionsublinear funcitonexistence criteria.

MSC classification

Secondary: 39A10: Difference equations, additive
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 1 , August 1999 , pp. 122 - 142
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Agarwal, R. P., Difference equations and inequalities (Academic Press, New York, 1992).Google Scholar
[2]Cheng, S. S. and Patula, W. T., ‘An existence theorem for a nonlinear difference equation’, Nonlinear Anal. 30 (1993), 193–203.CrossRefGoogle Scholar
[3]Cheng, S. S., Zhang, G. and Li, W. T., ‘On a higher order neutral difference equation’, Recent Trends in Math. Anal. Appl., to appear.Google Scholar
[4]Grace, S. R. and Lalli, B. S., ‘Oscillation theorems for second order delay and neutral difference equations’, Util. Math. 45 (1994), 199–211.Google Scholar
[5]He, X. Z., ‘Oscillation and asymptotic behavior of second order nonlinear difference equation’, J. Math. Anal. Appl. 175 (1993), 482–498.Google Scholar
[6]Kiguradze, I. T. and Chanturia, T. A., Asymptotic properties of solutions of nonautonomous ordinary differential equations (Kluwer, Amsterdam, 1993).Google Scholar
[7]Lalli, B. S., ‘Oscillation theorems for neutral difference equations’, Comput. Math. Appl. 28 (1994), 191–202.CrossRefGoogle Scholar
[8]Lalli, B. S. and Zhang, B. G., ‘On existence of positive solution and bounded oscillation for neutral difference equations’, J. Math. Anal. Appl. 166 (1992), 272–287.Google Scholar
[9]Lalli, B. S., Zhang, B. G. and Li, J. Z., ‘On the oscillation and existence of positive solutions of neutral difference equations’, J. Math. Anal. Appl. 158 (1991), 213–233.CrossRefGoogle Scholar
[10]Li, W. T. and Cheng, S. S., ‘Classifications and existence of positive solutions of second order nonlinear neutral difference equations’, Funkcial. Ekvac. 40 (1997), 371–393.Google Scholar
[11]Liu, B. and Yan, J. R., ‘Oscillation theorems for nonlinear neutral difference equations’, J. Differ. Equations Appl. 1 (1995), 307–315.CrossRefGoogle Scholar
[12]Smith, B. and Taylor, W. E. Jr, ‘Oscillatory and asymptotic behavior of certain fourth order difference equations’, Rocky Mountain J. Math. 16 (1986), 403–406.Google Scholar
[13]Zafer, A. and Dahiya, R., ‘Oscillation of a neutral difference equation’, Appl. Math. Lett. 6 (1993), 71–74.CrossRefGoogle Scholar
[14]Zhang, B. G. and Cheng, S. S., ‘On a class of nonlinear difference equations’, J. Differ. Equations Appl. 1 (1995), 391–411.Google Scholar
[15]Zhang, G. and Cheng, S. S., ‘Oscillation criteria for a neutral difference equation with delay’, Appl. Math. Lett. 8 (1995), 13–17.CrossRefGoogle Scholar
[16]Zhou, X. L. and Yan, J. R., ‘Oscillatory properties of higher order nonlinear difference equations’, Comput. Math. Appl. 31 (1996), 61–68.CrossRefGoogle Scholar