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Positive decreasing solutions of higher-order nonlinear difference equations. (English) Zbl 1198.39018
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:
39A22Growth, boundedness, comparison of solutions (difference equations)
39A10Additive difference equations
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