On the fundamental solution of linear delay differential equations with multiple delays
For a class of linear autonomous delay differential equations with parameter $\alpha$ we give upper bounds for the integral $\int_{0}^{\infty}\left|X\left(t,\alpha\right)\right|\mbox{d}t$ of the fundamental solution $X\left(\cdot,\alpha\right)$. The asymptotic estimations are sharp at a critical val...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2011-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=780 |
| _version_ | 1797830681496125440 |
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| author | Gabriella Vas Tibor Krisztin |
| author_facet | Gabriella Vas Tibor Krisztin |
| author_sort | Gabriella Vas |
| collection | DOAJ |
| description | For a class of linear autonomous delay differential equations with parameter $\alpha$ we give upper bounds for the integral $\int_{0}^{\infty}\left|X\left(t,\alpha\right)\right|\mbox{d}t$ of the fundamental solution $X\left(\cdot,\alpha\right)$. The asymptotic estimations are sharp at a critical value $\alpha_{0}$ where $x=0$ loses stability. We use these results to study the stability properties of perturbed equations. |
| first_indexed | 2024-04-09T13:41:02Z |
| format | Article |
| id | doaj.art-ec4fd2b7d6c54087958d02df277edaae |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:02Z |
| publishDate | 2011-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-ec4fd2b7d6c54087958d02df277edaae2023-05-09T07:53:01ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752011-06-0120113612810.14232/ejqtde.2011.1.36780On the fundamental solution of linear delay differential equations with multiple delaysGabriella Vas0Tibor Krisztin1MTA-SZTE Analysis and Stochastic Research Group, Bolyai Institute, University of Szeged, HungaryBolyai Institute, University of Szeged, Szeged, HungaryFor a class of linear autonomous delay differential equations with parameter $\alpha$ we give upper bounds for the integral $\int_{0}^{\infty}\left|X\left(t,\alpha\right)\right|\mbox{d}t$ of the fundamental solution $X\left(\cdot,\alpha\right)$. The asymptotic estimations are sharp at a critical value $\alpha_{0}$ where $x=0$ loses stability. We use these results to study the stability properties of perturbed equations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=780linear delay differential equationfundamental solutionlaplace transformdiscrete lyapunov functional |
| spellingShingle | Gabriella Vas Tibor Krisztin On the fundamental solution of linear delay differential equations with multiple delays Electronic Journal of Qualitative Theory of Differential Equations linear delay differential equation fundamental solution laplace transform discrete lyapunov functional |
| title | On the fundamental solution of linear delay differential equations with multiple delays |
| title_full | On the fundamental solution of linear delay differential equations with multiple delays |
| title_fullStr | On the fundamental solution of linear delay differential equations with multiple delays |
| title_full_unstemmed | On the fundamental solution of linear delay differential equations with multiple delays |
| title_short | On the fundamental solution of linear delay differential equations with multiple delays |
| title_sort | on the fundamental solution of linear delay differential equations with multiple delays |
| topic | linear delay differential equation fundamental solution laplace transform discrete lyapunov functional |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=780 |
| work_keys_str_mv | AT gabriellavas onthefundamentalsolutionoflineardelaydifferentialequationswithmultipledelays AT tiborkrisztin onthefundamentalsolutionoflineardelaydifferentialequationswithmultipledelays |