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Oscillation of a class of nonlinear neutral difference equations of higher order. (English) Zbl 1037.39002
The authors obtain sufficient conditions for the oscillation of the forced nonlinear neutral difference equation \[ \Delta y(n)+ p(n) G(y(n- k))= f(n) \] using a function \(F(n)\) satisfying \(\Delta^m F(n)= f(n)\). Existence of positive bounded solutions is also established. For the case where \(f(n)\equiv 0\), the behavior of solutions is studied separately.

MSC:
39A11 Stability of difference equations (MSC2000)
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