Trench's Perturbation Theorem for Dynamic Equations
We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/75672 |
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| _version_ | 1832553755041595392 |
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| author | Martin Bohner Stevo Stevic |
| author_facet | Martin Bohner Stevo Stevic |
| author_sort | Martin Bohner |
| collection | DOAJ |
| description | We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench. |
| format | Article |
| id | doaj-art-6f977d1f18d641c1a23c13d49808470a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6f977d1f18d641c1a23c13d49808470a2025-02-03T05:53:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/7567275672Trench's Perturbation Theorem for Dynamic EquationsMartin Bohner0Stevo Stevic1Department of Mathematics and Statistics, Missouri University of Science and Technology, MO 65401, USAMathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, Beograd 11000, SerbiaWe consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.http://dx.doi.org/10.1155/2007/75672 |
| spellingShingle | Martin Bohner Stevo Stevic Trench's Perturbation Theorem for Dynamic Equations Discrete Dynamics in Nature and Society |
| title | Trench's Perturbation Theorem for Dynamic Equations |
| title_full | Trench's Perturbation Theorem for Dynamic Equations |
| title_fullStr | Trench's Perturbation Theorem for Dynamic Equations |
| title_full_unstemmed | Trench's Perturbation Theorem for Dynamic Equations |
| title_short | Trench's Perturbation Theorem for Dynamic Equations |
| title_sort | trench s perturbation theorem for dynamic equations |
| url | http://dx.doi.org/10.1155/2007/75672 |
| work_keys_str_mv | AT martinbohner trenchsperturbationtheoremfordynamicequations AT stevostevic trenchsperturbationtheoremfordynamicequations |