## Global attractivity of a higher-order nonlinear difference equation.(English)Zbl 1201.39006

Authors’ abstract: The main goal of this paper is to investigate the locally asymptotically stable, period-two solutions, invariant intervals and global attractivity of all negative solutions of the nonlinear difference equation $x_{n+1} = \frac{1-x_n}{A+x_{n-k}}, \quad n=0,1,\dots ,$ where $$A\in (-\infty ,-1),k$$ is a positive integer and initial conditions $$x_{-k},\dots , x_0\in (-\infty ,0]$$. It is shown that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient

### MSC:

 39A20 Multiplicative and other generalized difference equations 39A30 Stability theory for difference equations 39A22 Growth, boundedness, comparison of solutions to difference equations
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### References:

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