On the periodic solutions of linear homogenous systems of differential equations
Given a fundamental matrix ϕ(x) of an n-th order system of linear homogeneous differential equations Y′=A(x)Y, a necessary and sufficient condition for the existence of a k-dimensional (k≤n) periodic sub-space (of period T) of the solution space of the above system is obtained in terms of the rank o...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000283 |
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| _version_ | 1832562868866777088 |
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| author | A. K. Bose |
| author_facet | A. K. Bose |
| author_sort | A. K. Bose |
| collection | DOAJ |
| description | Given a fundamental matrix ϕ(x) of an n-th order system of linear homogeneous differential equations Y′=A(x)Y, a necessary and sufficient condition for the existence of a k-dimensional (k≤n) periodic sub-space (of period T) of the solution space of the above system is obtained in terms of the rank of the scalar matrix ϕ(t)−ϕ(0). |
| format | Article |
| id | doaj-art-502481cadec5424e98dffe78ae492a15 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-502481cadec5424e98dffe78ae492a152025-02-03T01:21:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015230530910.1155/S0161171282000283On the periodic solutions of linear homogenous systems of differential equationsA. K. Bose0Department of Mathematical Sciences, Clemson University, Clemson 29613, South Carolina, USAGiven a fundamental matrix ϕ(x) of an n-th order system of linear homogeneous differential equations Y′=A(x)Y, a necessary and sufficient condition for the existence of a k-dimensional (k≤n) periodic sub-space (of period T) of the solution space of the above system is obtained in terms of the rank of the scalar matrix ϕ(t)−ϕ(0).http://dx.doi.org/10.1155/S0161171282000283linear homogeneous system of differential equationsfundamental matrixperiodic solutionsperiodic sub-spaces of (period T)rank of the scalar matrixlinearly independent vectors. |
| spellingShingle | A. K. Bose On the periodic solutions of linear homogenous systems of differential equations International Journal of Mathematics and Mathematical Sciences linear homogeneous system of differential equations fundamental matrix periodic solutions periodic sub-spaces of (period T) rank of the scalar matrix linearly independent vectors. |
| title | On the periodic solutions of linear homogenous systems of differential equations |
| title_full | On the periodic solutions of linear homogenous systems of differential equations |
| title_fullStr | On the periodic solutions of linear homogenous systems of differential equations |
| title_full_unstemmed | On the periodic solutions of linear homogenous systems of differential equations |
| title_short | On the periodic solutions of linear homogenous systems of differential equations |
| title_sort | on the periodic solutions of linear homogenous systems of differential equations |
| topic | linear homogeneous system of differential equations fundamental matrix periodic solutions periodic sub-spaces of (period T) rank of the scalar matrix linearly independent vectors. |
| url | http://dx.doi.org/10.1155/S0161171282000283 |
| work_keys_str_mv | AT akbose ontheperiodicsolutionsoflinearhomogenoussystemsofdifferentialequations |