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Oscillation and global attractivity in a nonlinear delay differential equation. (English) Zbl 0990.39013
Summary: We obtain a necessary and sufficient condition for every positive solution of the nonlinear delay difference equation \[ x_{n+1}=\frac {x_n}{a+bx_{n-k}^{p}-cx_{n-k}^{q}} , \qquad n=0,1,\dots \tag \(*\) \] to oscillate about its positive equilibrium. We also obtain conditions under which the positive equilibrium of \((*)\) is globally attractive.
MSC:
39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
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References:
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