Asymptotic Expansions for Higher-Order Scalar Difference Equations

被引：0
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作者：
Ravi P. Agarwal
Mihály Pituk
机构：
[1] Florida Institute of Technology,Department of Mathematical Sciences
[2] University of Veszprém,Department of Mathematics and Computing
来源：
Advances in Difference Equations | / 2007卷
关键词：
Differential Equation; Partial Differential Equation; Ordinary Differential Equation; Functional Analysis; Functional Equation;
D O I：
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摘要：
We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
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