On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations
Unimprovable efficient conditions are established for the existence and uniqueness of a nonnegative solution of the problem $$ u^{\prime}(t)=\ell(u)(t)+q(t), \ \ \ \ u(a)=h(u)+c, $$ where $\ell:C([a,b];\mathbb{R})\rightarrow L([a,b];\mathbb{R})$ is a linear bounded operator, $h:C([a,b];\mathbb{R})\...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2004-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=198 |
| _version_ | 1797830768137863168 |
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| author | A. Lomtatidze Zdenek Oplustil |
| author_facet | A. Lomtatidze Zdenek Oplustil |
| author_sort | A. Lomtatidze |
| collection | DOAJ |
| description | Unimprovable efficient conditions are established for the existence and uniqueness of a nonnegative solution of the problem
$$
u^{\prime}(t)=\ell(u)(t)+q(t), \ \ \ \ u(a)=h(u)+c,
$$
where $\ell:C([a,b];\mathbb{R})\rightarrow L([a,b];\mathbb{R})$ is a linear bounded operator, $h:C([a,b];\mathbb{R})\rightarrow \mathbb{R}$ is a linear bounded functional, $q\in L([a,b];\mathbb{R})$ and $c>0$. |
| first_indexed | 2024-04-09T13:41:25Z |
| format | Article |
| id | doaj.art-3a2eab7cd9f64423a094dad1704b7c8f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:25Z |
| publishDate | 2004-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-3a2eab7cd9f64423a094dad1704b7c8f2023-05-09T07:52:57ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752004-08-0120031612110.14232/ejqtde.2003.6.16198On nonnegative solutions of a certain boundary value problem for first order linear functional differential equationsA. Lomtatidze0Zdenek Oplustil1Institute of Mathematics, Academy of Sciences of the Czech RepublicBrno University of Technology, Brno, Czech RepublicUnimprovable efficient conditions are established for the existence and uniqueness of a nonnegative solution of the problem $$ u^{\prime}(t)=\ell(u)(t)+q(t), \ \ \ \ u(a)=h(u)+c, $$ where $\ell:C([a,b];\mathbb{R})\rightarrow L([a,b];\mathbb{R})$ is a linear bounded operator, $h:C([a,b];\mathbb{R})\rightarrow \mathbb{R}$ is a linear bounded functional, $q\in L([a,b];\mathbb{R})$ and $c>0$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=198 |
| spellingShingle | A. Lomtatidze Zdenek Oplustil On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations Electronic Journal of Qualitative Theory of Differential Equations |
| title | On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations |
| title_full | On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations |
| title_fullStr | On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations |
| title_full_unstemmed | On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations |
| title_short | On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations |
| title_sort | on nonnegative solutions of a certain boundary value problem for first order linear functional differential equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=198 |
| work_keys_str_mv | AT alomtatidze onnonnegativesolutionsofacertainboundaryvalueproblemforfirstorderlinearfunctionaldifferentialequations AT zdenekoplustil onnonnegativesolutionsofacertainboundaryvalueproblemforfirstorderlinearfunctionaldifferentialequations |