Geodesic
Some Oscillatory Properties for a Class of Partial Difference Equations
Ma, Huili1 ; Wang, Jiaofeng1
1 Department of Mathematics, Northwest Normal University, Lanzhou Gansu 730070, P. R. China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 6, p. 3473-3478.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper we study the oscillatory property of solutions for a class of partial difference equation with constant coefficients. In order to study the oscillation results, we find the regions of nonexistence of positive roots of its characteristic equation which is equivalent to the oscillation results. We derive some necessary and sufficient conditions by means of the envelope theory.
DOI : 10.22436/jnsa.009.06.02
Classification : 47H10, 54H25
Keywords: Partial difference equation, oscillation, envelope, characteristic equation.

Ma, Huili 1 ; Wang, Jiaofeng 1

1 Department of Mathematics, Northwest Normal University, Lanzhou Gansu 730070, P. R. China 
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Ma, Huili; Wang, Jiaofeng. Some Oscillatory Properties for a Class of Partial Difference Equations. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 6, p. 3473-3478. doi : 10.22436/jnsa.009.06.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.06.02/

[1] Agarwal, R. P.; Grace, S. R.; O'Regan, D. Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 2003

[2] Agarwal, R. P.; Y. Zhou Oscillation of partial difference equations with continuous variables, Math. Comput. Modelling, Volume 31 (2000), pp. 17-29

[3] Berman, G.; K. D. Fryer Introduction to Combinatorics, Academic Press, New York-London, 1972

[4] Cheng, S. S. Partial Difference Equations, Advances in Discrete Mathematics and Applications, Taylor and Francis, London, 2003

[5] Cheng, S. S.; Lin, Y. Z. Dual sets of envelopes and characteristic regions of quasi-polynomials, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2009

[6] LeVeque, R. J. Numerical Methods for Conservation Laws, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1990

[7] X.-P. Li Partial difference equations used in the study of molecularorbits, Acta Chimica SINICA, Volume 40 (1982), pp. 688-698

[8] Meakin, P. Models for material failure and deformation, Science, Volume 252 (1991), pp. 226-234

[9] Shi, B. E.; Chua, L. O. Resistive grid image filtering: input/output analysis via the CNN framework, Fund. Theory Appl., IEEE Trans., Volume 39 (1992), pp. 531-548

[10] Strikwerda, J. C. Finite difference schemes and partial difference equations, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1989

[11] Yuan, C. H.; Liu, S. T. An envelope surface method for determining oscillation of a delay 2-D discrete convection system, J. Dynam. Differential Equation, Volume 2014 (2014), pp. 1-16

[12] Zhang, B. G.; Agarwal, R. P. The oscillation and stability of delay partial difference equations, Comput. Math. Appl., Volume 45 (2003), pp. 1253-1295

[13] Zhang, B. G.; Xing, Q. Oscillation of certain partial difference equations, J. Math. Anal. Appl., Volume 329 (2007), pp. 567-580

[14] Zhang, B. G.; Yu, J. S. Linearized oscillation theorems for certain nonlinear delay partial difference equations, Comput. Math. Appl., Volume 35 (1998), pp. 111-116

[15] Zhang, B.; Zhou, Y. Qualitative analysis of delay partial difference equations, Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, 2007

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