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| Title: | Asymptotic expansion and analytic dynamic equations |
| Author (s): | Bohner, Martin Lutz, Donald A. |
| Department/Lab Affiliations: | Mathematics & Statistics |
| Keywords: | Dichotomy condition Growth condition Perturbation result Time scale |
| Issue Date: | 2006 |
| Publisher: | Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim |
| Citation: | Bohner, Martin., and Lutz, Donald A. "Asymptotic Expansion and Analytic Dynamic Equations." ZAMM Journal of Applied Mathematics and Mechanics, vol. 86, no. 1, pp. 37-45 (2006). |
| Abstract: | Time scales have been introduced in order to unify the theories of differential and difference equations and in order to extend these cases to many other so-called dynamic equations. In this paper we consider a linear dynamic equation on a time scale together with a perturbed equation. We show that, if certain exponential dichotomy conditions are satisfied, then for any solution of the perturbed equation there exists a solution of the unperturbed equation that asymptotically differs from the solution of the perturbed equation no more than the order of the perturbation term. In order to show this perturbation theorem, we use many properties of the exponential function on time scales and derive several bounds for certain monomials that appear in the dynamic version of Taylor's formula. |
| Type: | Article - Journal text |
| In Title: | ZAMM Journal of Applied Mathematics and Mechanics |
| Copyright Notice: | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. FULL COPYRIGHT INFORMATION: |
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| title | Asymptotic expansion and analytic dynamic equations |
| contributor.author | Bohner, Martin |
| contributor.author | Lutz, Donald A. |
| contributor.deptlab | Mathematics & Statistics |
| subject | Dichotomy condition |
| subject | Growth condition |
| subject | Perturbation result |
| subject | Time scale |
| date.issued | 2006 |
| publisher | Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim |
| identifier.citation | Bohner, Martin., and Lutz, Donald A. "Asymptotic Expansion and Analytic Dynamic Equations." ZAMM Journal of Applied Mathematics and Mechanics, vol. 86, no. 1, pp. 37-45 (2006). |
| identifier.pub.URI | |
| description.abstract | Time scales have been introduced in order to unify the theories of differential and difference equations and in order to extend these cases to many other so-called dynamic equations. In this paper we consider a linear dynamic equation on a time scale together with a perturbed equation. We show that, if certain exponential dichotomy conditions are satisfied, then for any solution of the perturbed equation there exists a solution of the unperturbed equation that asymptotically differs from the solution of the perturbed equation no more than the order of the perturbation term. In order to show this perturbation theorem, we use many properties of the exponential function on time scales and derive several bounds for certain monomials that appear in the dynamic version of Taylor's formula. |
| type | Article - Journal |
| type.DCMIType | text |
| type.status | Final version |
| rights | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. |
| rights.URI | |
| relation.isPartOf | ZAMM Journal of Applied Mathematics and Mechanics |
| date.accessioned | 2007-04-11T17:00:48Z |
| date.available | 2008-04-22T18:26:34Z |
| identifier.persist.URI |