Existence of nontrivial solutions of a rational difference equation (Q2463917)
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| Language | Label | Description | Also known as |
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| English | Existence of nontrivial solutions of a rational difference equation |
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Existence of nontrivial solutions of a rational difference equation (English)
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6 December 2007
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The author determines the asymptotic behaviour of a special solution of \[ x_{n+1}= (x_n+ x_{n-1}+ x_{n-2} x_{n-3})/(x_n x_{n-1}+ x_{n-2}+ x_{n-3}) \] which confirms a conjecture of \textit{L. Ladas} [J. Difference Equ. Appl. 4, No. 5, 497--499 (1998; Zbl 0925.39004)] concerning the existence of a solution being not eventually constant.
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Putnam difference equation
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global asymptotic stability
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equilibrium point
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positive solution
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nontrivial solutions
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