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Zbl 1198.39018
Krasznai, B.; Gy\H{o}ri, I.; Pituk, M.
Positive decreasing solutions of higher-order nonlinear difference equations. (English)
[J] Adv. Difference Equ. 2010, Article ID 973432, 16 p. (2010). ISSN 1687-1847/e

Summary: It is shown that the decay rates of the positive, monotone decreasing solutions approaching the zero equilibrium of higher-order nonlinear difference equations are related to the positive characteristic values of the corresponding linearized equation. If the nonlinearity is sufficiently smooth, this result yields an asymptotic formula for the positive, monotone decreasing solutions.
MSC 2000:
*39A22
39A10 Difference equations

Keywords: higher-order nonlinear difference equations; positive characteristic values; asymptotic formula; positive, monotone decreasing solutions

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