Differentiability of solutions with respect to the delay function in functional differential equations
In this paper we consider a class of functional differential equations with time-dependent delay. We show continuous differentiability of the solution with respect to the time delay function for each fixed time value assuming natural conditions on the delay function. As an application of the differe...
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5290 |
| _version_ | 1797830583716413440 |
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| author | Ferenc Hartung |
| author_facet | Ferenc Hartung |
| author_sort | Ferenc Hartung |
| collection | DOAJ |
| description | In this paper we consider a class of functional differential equations with time-dependent delay. We show continuous differentiability of the solution with respect to the time delay function for each fixed time value assuming natural conditions on the delay function. As an application of the differentiability result, we give a numerical study to estimate the time delay function using the quasilinearization method. |
| first_indexed | 2024-04-09T13:38:25Z |
| format | Article |
| id | doaj.art-72064cc52d3440bc93c193344d8383bb |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:25Z |
| publishDate | 2016-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-72064cc52d3440bc93c193344d8383bb2023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-09-0120167311610.14232/ejqtde.2016.1.735290Differentiability of solutions with respect to the delay function in functional differential equationsFerenc Hartung0Department of Mathematics, University of Pannonia, Veszprém, HungaryIn this paper we consider a class of functional differential equations with time-dependent delay. We show continuous differentiability of the solution with respect to the time delay function for each fixed time value assuming natural conditions on the delay function. As an application of the differentiability result, we give a numerical study to estimate the time delay function using the quasilinearization method.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5290delay differential equationtime-dependent delaydifferentiability with respect to parameters |
| spellingShingle | Ferenc Hartung Differentiability of solutions with respect to the delay function in functional differential equations Electronic Journal of Qualitative Theory of Differential Equations delay differential equation time-dependent delay differentiability with respect to parameters |
| title | Differentiability of solutions with respect to the delay function in functional differential equations |
| title_full | Differentiability of solutions with respect to the delay function in functional differential equations |
| title_fullStr | Differentiability of solutions with respect to the delay function in functional differential equations |
| title_full_unstemmed | Differentiability of solutions with respect to the delay function in functional differential equations |
| title_short | Differentiability of solutions with respect to the delay function in functional differential equations |
| title_sort | differentiability of solutions with respect to the delay function in functional differential equations |
| topic | delay differential equation time-dependent delay differentiability with respect to parameters |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5290 |
| work_keys_str_mv | AT ferenchartung differentiabilityofsolutionswithrespecttothedelayfunctioninfunctionaldifferentialequations |