On the oscillation of a nonlinear two-dimensional difference systems | Zendy

E. Thandapani | Zendy; B. Ponnammal | Zendy

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On the oscillation of a nonlinear two-dimensional difference systems

Author(s) -

E. Thandapani,

B. Ponnammal

Publication year - 2001

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.32.2001.375

Subject(s) - sublinear function , mathematics , integer (computer science) , oscillation (cell signaling) , combinatorics , sequence (biology) , nonlinear system , mathematical analysis , physics , quantum mechanics , biology , computer science , genetics , programming language

The authors consider the two-dimensional difference system

$$ Delta x_n = b_n g (y_n) $$

$$ Delta y_n = -f(n, x_{n+1}) $$

where $ n in N(n_0) = { n_0, n_0+1, ldots } $, $ n_0 $ a nonnegative integer; $ { b_n } $ is a real sequence, $ f: N(n_0) imes {m R} o {m R} $ is continuous with $ u f(n,u) > 0 $ for all $ u e 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

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