Abstract
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.
Highlights
Introduction and the Main ResultsLet R, C, and Z be the set of real and complex numbers and the set of integers, respectively
The symbol Z denotes the set of nonnegative integers
For the second-order equation 1.1, we have the following theorem which provides new information about the decreasing fast solutions obtained by Aprahamian et al 1
Summary
Introduction and the Main ResultsLet R, C, and Z be the set of real and complex numbers and the set of integers, respectively. The main result of 1 is the following theorem about the existence of positive, decreasing solutions of 1.1 see 1, Theorem 1.2 and its proof . Our result, combined with asymptotic theorems from 2 or 3 , yields asymptotic formulas for the positive, monotone decreasing solutions of 1.6 .
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