Article
| Title: | Stieltjes differential problems with general boundary value conditions. Existence and bounds of solutions (English) |
| Author: | Marraffa, Valeria |
| Author: | Satco, Bianca |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 235-255 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We are concerned with first order set-valued problems with very general boundary value conditions $$ \begin{cases} u'_g(t)\in F(t,u(t)),\quad \mu _g \text {-a.e.} \t\in [0,T] , \\ L(u(0),\u(T))=0 \end{cases} $$ involving the Stieltjes derivative with respect to a left-continuous nondecreasing function $g\colon [0,T]\to \mathbb {R}$, a Carathéodory multifunction $F\colon [0,T]\times \mathbb {R}\to \mathcal {P}(\mathbb {R})$ and a continuous $L\colon \mathbb {R}^2\to \mathbb {R}$. Using appropriate notions of lower and upper solutions, we prove the existence of solutions via a fixed point result for condensing mappings. In the periodic single-valued case, combining an existence theory for the linear case with a recent result involving lower and upper solutions (which can be seen as a consequence of our existence theorem mentioned before), we get not only the existence of solutions, but also lower and upper bounds, respectively, by imposing an estimation for the right-hand side. (English) |
| Keyword: | boundary value differential inclusion |
| Keyword: | Stieltjes derivative |
| Keyword: | Kurzweil-Stieltjes integral |
| Keyword: | periodic problem |
| MSC: | 26A24 |
| MSC: | 26A42 |
| MSC: | 34A06 |
| MSC: | 34B15 |
| MSC: | 47H10 |
| DOI: | 10.21136/CMJ.2024.0125-23 |
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| Date available: | 2025-03-11T16:02:15Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152906 |
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