Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations
In the present paper, we are concerned with a very general problem, namely the Stieltjes differential Cauchy problem involving state-dependent discontinuities. Given that the theory of Stieltjes differential equations covers the framework of impulsive problems with fixed-time impulses, in the prese...
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| Format: | Article |
| Language: | English |
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University of Szeged
2022-07-01
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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=9766 |
| _version_ | 1797830440831156224 |
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| author | Bianca Satco |
| author_facet | Bianca Satco |
| author_sort | Bianca Satco |
| collection | DOAJ |
| description | In the present paper, we are concerned with a very general problem, namely the Stieltjes differential Cauchy problem involving state-dependent discontinuities.
Given that the theory of Stieltjes differential equations covers the framework of impulsive problems with fixed-time impulses, in the present work we generalize this setting by allowing the occurrence of fixed-time impulses, as well as the occurrence of state-dependent impulses.
Along with an existence result obtained under an overarching set of assumptions involving Stieltjes integrals, it is showed that a least and a greatest solution can be found. |
| first_indexed | 2024-04-09T13:36:05Z |
| format | Article |
| id | doaj.art-6d5c1bcdac234c499338393f256cba51 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:05Z |
| publishDate | 2022-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-6d5c1bcdac234c499338393f256cba512023-05-09T07:53:12ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752022-07-0120222811710.14232/ejqtde.2022.1.289766Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equationsBianca Satco0Stefan cel Mare University, Suceava, RomaniaIn the present paper, we are concerned with a very general problem, namely the Stieltjes differential Cauchy problem involving state-dependent discontinuities. Given that the theory of Stieltjes differential equations covers the framework of impulsive problems with fixed-time impulses, in the present work we generalize this setting by allowing the occurrence of fixed-time impulses, as well as the occurrence of state-dependent impulses. Along with an existence result obtained under an overarching set of assumptions involving Stieltjes integrals, it is showed that a least and a greatest solution can be found.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9766stieltjes differential equationstate-dependent impulsive equationstieltjes integralextremal solution |
| spellingShingle | Bianca Satco Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations Electronic Journal of Qualitative Theory of Differential Equations stieltjes differential equation state-dependent impulsive equation stieltjes integral extremal solution |
| title | Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations |
| title_full | Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations |
| title_fullStr | Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations |
| title_full_unstemmed | Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations |
| title_short | Fixed-time and state-dependent time discontinuities in the theory of Stieltjes differential equations |
| title_sort | fixed time and state dependent time discontinuities in the theory of stieltjes differential equations |
| topic | stieltjes differential equation state-dependent impulsive equation stieltjes integral extremal solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9766 |
| work_keys_str_mv | AT biancasatco fixedtimeandstatedependenttimediscontinuitiesinthetheoryofstieltjesdifferentialequations |