Oscillations of a nonlinear third order difference equation. (English) Zbl 1052.39006
The authors consider the third order nonlinear delay difference equations
\[
x_{n+1}=f(x_n,x_{n-1},x_{n-2}).
\]
They study the oscillation behavior of the solutions and the lengths of the semicycles. The results are applied to the nonlinear delay difference equation
\[
x_{n+1}=\frac{a+x_n^b}{x_{n-1}^s x_{n-1}^q}
\]
and some sufficient conditions for oscillation of all solutions about the positive steady state are established.
Reviewer: Samir H. Saker (Mansoura)
MSC:
39A11 | Stability of difference equations (MSC2000) |
39A20 | Multiplicative and other generalized difference equations |