Open AccessOn 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.