Notes on the linear equation with Stieltjes derivatives
In this paper we continue the study of the linear equation with Stieltjes derivatives in [M. Frigon, R. López Pouso, Adv. Nonlinear Anal. 6(2017), 13–36]. Specifically, we revisit some of the results there presented, removing some of the required conditions as well as amending some mistakes. Further...
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| Format: | Article |
| Language: | English |
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University of Szeged
2021-06-01
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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=8851 |
| _version_ | 1797830440173699072 |
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| author | Ignacio Márquez Albés |
| author_facet | Ignacio Márquez Albés |
| author_sort | Ignacio Márquez Albés |
| collection | DOAJ |
| description | In this paper we continue the study of the linear equation with Stieltjes derivatives in [M. Frigon, R. López Pouso, Adv. Nonlinear Anal. 6(2017), 13–36]. Specifically, we revisit some of the results there presented, removing some of the required conditions as well as amending some mistakes. Furthermore, following the classical setting, we use the connection between the linear equation and the Gronwall inequality to obtain a new version of this type of inequalities in the context of Lebesgue–Stieltjes integrals. From there, we obtain a uniqueness criterion for initial value problems. |
| first_indexed | 2024-04-09T13:37:17Z |
| format | Article |
| id | doaj.art-667b89e0c57b4bc38113b2d94265f531 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:17Z |
| publishDate | 2021-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-667b89e0c57b4bc38113b2d94265f5312023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-06-0120214211810.14232/ejqtde.2021.1.428851Notes on the linear equation with Stieltjes derivativesIgnacio Márquez Albés0Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, SpainIn this paper we continue the study of the linear equation with Stieltjes derivatives in [M. Frigon, R. López Pouso, Adv. Nonlinear Anal. 6(2017), 13–36]. Specifically, we revisit some of the results there presented, removing some of the required conditions as well as amending some mistakes. Furthermore, following the classical setting, we use the connection between the linear equation and the Gronwall inequality to obtain a new version of this type of inequalities in the context of Lebesgue–Stieltjes integrals. From there, we obtain a uniqueness criterion for initial value problems.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8851stieltjes integrationstieltjes differentiationlinear equationuniquenessgronwall inequality |
| spellingShingle | Ignacio Márquez Albés Notes on the linear equation with Stieltjes derivatives Electronic Journal of Qualitative Theory of Differential Equations stieltjes integration stieltjes differentiation linear equation uniqueness gronwall inequality |
| title | Notes on the linear equation with Stieltjes derivatives |
| title_full | Notes on the linear equation with Stieltjes derivatives |
| title_fullStr | Notes on the linear equation with Stieltjes derivatives |
| title_full_unstemmed | Notes on the linear equation with Stieltjes derivatives |
| title_short | Notes on the linear equation with Stieltjes derivatives |
| title_sort | notes on the linear equation with stieltjes derivatives |
| topic | stieltjes integration stieltjes differentiation linear equation uniqueness gronwall inequality |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8851 |
| work_keys_str_mv | AT ignaciomarquezalbes notesonthelinearequationwithstieltjesderivatives |