Necessary and Sufficient Conditions for Oscillations of a Class of Mixed Partial Difference Equations

Abstract:

Various problems of science and engineering that deal with dynamical systems can be described by partial difference equations. This article is concerned with a class of mixed partial difference equations with constant coefficients. We obtain necessary and sufficient conditions for all solutions of these equations to be oscillatory by finding the characteristic roots. An example is given to illustrate the results presented in this paper.

• Periodical: Advanced Materials Research (Volumes 816-817)
• Pages: 3-6
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.816-817.3
• Online since: September 2013
• Authors: Chun Hua Yuan
• Keywords: Characteristic Equation, Oscillation, Partial Difference Equation

References

[1] X. P. Li: Acta Chimica Sinica vol. 40(1982), p.688.

[2] R. Courant, K. Friedrichs, and H. Lewy: IBM Journal of Research and Development, vol. 11(1967), p.215.

[3] J. C. Strikwerda: Finite Difference Schemes and Partial Difference Equations (Wadsworth, USA 1989).

[4] W. G. Kelly and A. C. Peterson: Difference Equations (Academic Press, USA 1991).

[5] B. G. Zhang and S. T. Liu: Differential Inclusions, vol. 15(1995), p.213.

[6] B.G. Zhang and S.T. Liu: Nonlinear Studies, vol. 3(1996), p.187.

[7] S. T. Liu and H. Wang: Dynamic Systems and Applications, vol. 7(1998), p.495.

[8] B. G. Zhang and S. T. Liu: Discrete Dynamics in Nature and Society, vol. 1(1998), p.265.

[9] B. G. Zhang and R. P. Agarwal: Computers & Mathematics with Applications, vol. 45(2003), p.1253.

[10] B. G. Zhang and Y. Zhou: Qualitative Analysis of Delay Partial Difference Equations (Hindawi Publishing Corporation, USA 2007).