Asymptotic Expansions for Higher-Order Scalar Difference Equations
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2007-04-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2007/67492 |
| _version_ | 1818134551353884672 |
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| author | Ravi P. Agarwal Mihály Pituk |
| author_facet | Ravi P. Agarwal Mihály Pituk |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T09:10:25Z |
| format | Article |
| id | doaj.art-a2a816ef09984e9d8acd94944a3cb26c |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T09:10:25Z |
| publishDate | 2007-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-a2a816ef09984e9d8acd94944a3cb26c2022-12-22T01:13:30ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472007-04-01200710.1155/2007/67492Asymptotic Expansions for Higher-Order Scalar Difference EquationsRavi P. AgarwalMihály PitukWe 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.http://dx.doi.org/10.1155/2007/67492 |
| spellingShingle | Ravi P. Agarwal Mihály Pituk Asymptotic Expansions for Higher-Order Scalar Difference Equations Advances in Difference Equations |
| title | Asymptotic Expansions for Higher-Order Scalar Difference Equations |
| title_full | Asymptotic Expansions for Higher-Order Scalar Difference Equations |
| title_fullStr | Asymptotic Expansions for Higher-Order Scalar Difference Equations |
| title_full_unstemmed | Asymptotic Expansions for Higher-Order Scalar Difference Equations |
| title_short | Asymptotic Expansions for Higher-Order Scalar Difference Equations |
| title_sort | asymptotic expansions for higher order scalar difference equations |
| url | http://dx.doi.org/10.1155/2007/67492 |
| work_keys_str_mv | AT ravipagarwal asymptoticexpansionsforhigherorderscalardifferenceequations AT mih225lypituk asymptoticexpansionsforhigherorderscalardifferenceequations |