Open AccessOscillation for nonlinear delay difference equations
Author(s) -
Xiao Tang
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.32.2001.342
Subject(s) - sublinear function , oscillation (cell signaling) , mathematics , nonlinear system , mathematical analysis , order (exchange) , physics , quantum mechanics , genetics , finance , economics , biology
The oscillatory behavior of the first order nonlinear delay difference equation of the form
$$ x_{n+1} - x_n + p_n x_{n-k}^{alpha} = 0, ~~~ n = 0, 1, 2, ldots eqno{(*)} $$
is investigated. A necessary and sufficient condition of oscillation for sublinear equation (*) ($ 0 < alpha < 1 $) and an almost sharp sufficient condition of oscillation for superlinear equation (*) ($ alpha > 1 $) are obtained.