On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$
In this paper we provide necesssary and sufficient conditions for the existence of at least one $\Psi$-bounded solution on $\mathbb{R}$ for the system $X'=A(t)X +XB(t)+F(t)$, where $F(t)$ is a Lebesgue $\Psi$-integrable matrix valued function on $\mathbb{R}$. Further, we prove a result relatin...
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| Format: | Article |
| Language: | English |
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University of Szeged
2009-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=449 |
| _version_ | 1797830727942799360 |
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| author | M. S. N. Murty Grande Suresh Kumar |
| author_facet | M. S. N. Murty Grande Suresh Kumar |
| author_sort | M. S. N. Murty |
| collection | DOAJ |
| description | In this paper we provide necesssary and sufficient conditions for the existence of at least one $\Psi$-bounded solution on $\mathbb{R}$ for the system $X'=A(t)X +XB(t)+F(t)$, where $F(t)$ is a Lebesgue $\Psi$-integrable matrix valued function on $\mathbb{R}$. Further, we prove a result relating to the asymptotic behavior of the $\Psi$-bounded solutions of this system. |
| first_indexed | 2024-04-09T13:41:49Z |
| format | Article |
| id | doaj.art-9a50d1c3f2a146dd85d1522a32f8cb96 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:49Z |
| publishDate | 2009-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-9a50d1c3f2a146dd85d1522a32f8cb962023-05-09T07:52:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752009-11-0120096211210.14232/ejqtde.2009.1.62449On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$M. S. N. Murty0Grande Suresh Kumar1Department of Mathematics, Acharya Nagarjuna University - NagarjunaNagar Guntur- 522510, India.Koneru Lakshmaiah University, Vaddeswaram, IndiaIn this paper we provide necesssary and sufficient conditions for the existence of at least one $\Psi$-bounded solution on $\mathbb{R}$ for the system $X'=A(t)X +XB(t)+F(t)$, where $F(t)$ is a Lebesgue $\Psi$-integrable matrix valued function on $\mathbb{R}$. Further, we prove a result relating to the asymptotic behavior of the $\Psi$-bounded solutions of this system.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=449 |
| spellingShingle | M. S. N. Murty Grande Suresh Kumar On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$ Electronic Journal of Qualitative Theory of Differential Equations |
| title | On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$ |
| title_full | On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$ |
| title_fullStr | On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$ |
| title_full_unstemmed | On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$ |
| title_short | On $\Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $\mathbb{R}$ |
| title_sort | on psi bounded solutions for non homogeneous matrix lyapunov systems on mathbb r |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=449 |
| work_keys_str_mv | AT msnmurty onpsiboundedsolutionsfornonhomogeneousmatrixlyapunovsystemsonmathbbr AT grandesureshkumar onpsiboundedsolutionsfornonhomogeneousmatrixlyapunovsystemsonmathbbr |