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Zbl 1169.39004
Medina, Rigoberto; Pituk, Mihály
Nonoscillatory solutions of a second-order difference equation of Poincaré type.
(English)
[J] Appl. Math. Lett. 22, No. 5, 679-683 (2009). ISSN 0893-9659

For the difference equation $$x_{n+2}+b_nx_{n+1}+c_nx_n=0$$ with real coefficients satisfying $b_n\to\beta<0$, $c_n\to\beta^2/4$ as $n \to\infty$, it is shown that every non-oscillatory solution has the Poincaré property $\frac{x_{n+1}}{x_n}\to\beta$. Note that $\beta$ is a double zero of the corresponding characteristic equation.
[Lothar Berg (Rostock)]
MSC 2000:
*39A11 Stability of difference equations
39A10 Difference equations

Keywords: second-order difference equation; Poincaré's theorem; non-oscillatory solution; asymptotic behavior

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