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A note on a generalization of Pielou’s equation. (English) Zbl 1151.39008
This work deals with the asymptotic behavior of solutions to the generalized Pielou equation \[ x_{n+1}=x_nf(x_{n-1})+c, \] where \(c\geq 0\) and \(f: [0, \infty)\to (0, \infty)\). The author shows that if \(f\) is continuous with some monotonicity properties similar to those of \(\frac{\beta}{1+x}\), then every solution converges to an equilibrium of the generalized Pielou equation.

MSC:
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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[1] DOI: 10.1016/j.jmaa.2006.10.096 · Zbl 1120.39003 · doi:10.1016/j.jmaa.2006.10.096
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