Oscillations of nonlinear partial difference systems

3Citations
Citations of this article
3Readers
Mendeley users who have this article in their library.
Get full text

Abstract

This paper studies the following two-dimensional nonlinear partial difference systems {T(∇1, ∇2) (xmn) + bmng(ymn) = 0, {T(Δ1, Δ2)(ymn) + amnf(xmn) = 0, where m, n ε N0= {0, 1, 2,...}, T(Δ1, Δ2) = Δ1+ Δ2+ I, T(∇1, ∇2) = ∇1+ ∇2+ I, Δ1ymn= ym+1,n- ymn, Δ2ymn= ym,n+1- ymn, Iymn= ymn, ∇1ymn= ym-1,n- ymn, ∇2ymn= ym,n-1- ymn, {amn} and {bmn} are real sequences, m, n ε N0, and f, g: R → R are continuous with uf (u) > 0 and ug(u) > 0 for all u ≠ 0. A solution ({xmn}, {ymn}) of the system is oscillatory if both components are oscillatory. Some sufficient conditions for all solutions of this system to be oscillatory are derived. © 2002 Elsevier Science (USA). All rights reserved.

Cite

CITATION STYLE

APA

Liu, S. T., & Chen, G. (2003). Oscillations of nonlinear partial difference systems. Journal of Mathematical Analysis and Applications, 277(2), 689–700. https://doi.org/10.1016/S0022-247X(02)00620-0

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free