Oscillation theorems for neutral difference equations. (English) Zbl 0807.39004

Lalli, B. S.

Comput. Math. Appl. 28, No. 1-3, 191-202 (1994).

The author oscillation criteria for first-order difference equations of the form \(\Delta x_ n + g_ n f(x_{n - r}) = 0\), \(\Delta (x_ n + px_{n - \delta k}) + g_ n f(x_{n-r}) = F_ n\) where \(\Delta x_ n = x_{n + 1} - x_ n\), \(\delta = \pm 1\), \(p\) is a real number, \(r\) and \(k\) are nonnegative integers, \(\{q_ n\}\), \(\{F_ n\}\) are sequences of nonnegative real numbers and \(f : \mathbb{R} \to \mathbb{R}\) is continuous. Oscillation criteria for nonlinear difference equation, of sublinear as well as superlinear type, are also established.

Reviewer: S.Balint (Timişoara)

MSC:

39A10

Additive difference equations

Keywords:

neutral difference equations; oscillation; first-order difference equations; nonlinear difference equation; sublinear; superlinear

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