Oscillation for nonlinear delay difference equations | Zendy

Xilian Tang | Zendy

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Oscillation for nonlinear delay difference equations

Author(s) -

Xilian 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.

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