Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations
Abstract We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the bilinear difference equation in terms of a solution to an associate difference eq...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1930-2 |
| _version_ | 1818188124749037568 |
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| author | Stevo Stević |
| author_facet | Stevo Stević |
| author_sort | Stevo Stević |
| collection | DOAJ |
| description | Abstract We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the bilinear difference equation in terms of a solution to an associate difference equation of second order, considerably generalizing some recent results in an elegant way. We also present the corresponding representations for some systems of bilinear difference equations. Many historical notes not so known to wide audience are also presented, and we offer an answer to an open question regarding the attribution of the bilinear difference equation. |
| first_indexed | 2024-12-11T23:21:56Z |
| format | Article |
| id | doaj.art-fd03076030ac4a29a17107dde02f72dc |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T23:21:56Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-fd03076030ac4a29a17107dde02f72dc2022-12-22T00:46:20ZengSpringerOpenAdvances in Difference Equations1687-18472018-12-012018112110.1186/s13662-018-1930-2Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equationsStevo Stević0Mathematical Institute of the Serbian Academy of SciencesAbstract We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the bilinear difference equation in terms of a solution to an associate difference equation of second order, considerably generalizing some recent results in an elegant way. We also present the corresponding representations for some systems of bilinear difference equations. Many historical notes not so known to wide audience are also presented, and we offer an answer to an open question regarding the attribution of the bilinear difference equation.http://link.springer.com/article/10.1186/s13662-018-1930-2Linear difference equationBilinear difference equationGeneral solutionRepresentation of solutionsSystem of bilinear difference equationsHistory of difference equations |
| spellingShingle | Stevo Stević Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations Advances in Difference Equations Linear difference equation Bilinear difference equation General solution Representation of solutions System of bilinear difference equations History of difference equations |
| title | Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations |
| title_full | Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations |
| title_fullStr | Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations |
| title_full_unstemmed | Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations |
| title_short | Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations |
| title_sort | representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations |
| topic | Linear difference equation Bilinear difference equation General solution Representation of solutions System of bilinear difference equations History of difference equations |
| url | http://link.springer.com/article/10.1186/s13662-018-1930-2 |
| work_keys_str_mv | AT stevostevic representationsofsolutionstolinearandbilineardifferenceequationsandsystemsofbilineardifferenceequations |