On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments
In this paper we consider the differential system (1.1) $u_i'(t)=f_i\big(t,u_1(\tau_{i1}(t)),u_2(\tau_{i2}(t))\big) (i=1,2)$ with the boundary conditions (1.2) $\varphi\big(u_1(0),u_2(0)\big)=0, u_1(t)=u_1(a), u_2(t)=0 for t\geq a,$ where $f_i: [0,a]\times \Bbb{R}^2\to \Bbb{R}$ $(i=1,2)$ satisf...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
1999-01-01
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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=1 |
| _version_ | 1797830761624109056 |
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| author | Ivan Kiguradze Nino Partsvania |
| author_facet | Ivan Kiguradze Nino Partsvania |
| author_sort | Ivan Kiguradze |
| collection | DOAJ |
| description | In this paper we consider the differential system (1.1)
$u_i'(t)=f_i\big(t,u_1(\tau_{i1}(t)),u_2(\tau_{i2}(t))\big) (i=1,2)$
with the boundary conditions (1.2)
$\varphi\big(u_1(0),u_2(0)\big)=0, u_1(t)=u_1(a), u_2(t)=0 for t\geq a,$
where $f_i: [0,a]\times \Bbb{R}^2\to \Bbb{R}$ $(i=1,2)$ satisfy the local Carathéodory conditions, while $\varphi: \Bbb{R}^2\to \Bbb{R}$ and $\tau_{ik}: [0,a]\to [0,+\infty[$ $(i,k=1,2)$ are continuous functions. The optimal, in a certain sense, sufficient conditions are obtained for the existence and uniqueness of a nonnegative solution of the problem (1.1), (1.2). |
| first_indexed | 2024-04-09T13:42:21Z |
| format | Article |
| id | doaj.art-22f15717dfd0442295597d1d72b371bd |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:42:21Z |
| publishDate | 1999-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-22f15717dfd0442295597d1d72b371bd2023-05-09T07:52:56ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751999-01-011999512210.14232/ejqtde.1999.1.51On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced argumentsIvan Kiguradze0Nino Partsvania1A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, Tbilisi, GeorgiaA. Razmadze Mathematical Institute, Tbilisi, GeorgiaIn this paper we consider the differential system (1.1) $u_i'(t)=f_i\big(t,u_1(\tau_{i1}(t)),u_2(\tau_{i2}(t))\big) (i=1,2)$ with the boundary conditions (1.2) $\varphi\big(u_1(0),u_2(0)\big)=0, u_1(t)=u_1(a), u_2(t)=0 for t\geq a,$ where $f_i: [0,a]\times \Bbb{R}^2\to \Bbb{R}$ $(i=1,2)$ satisfy the local Carathéodory conditions, while $\varphi: \Bbb{R}^2\to \Bbb{R}$ and $\tau_{ik}: [0,a]\to [0,+\infty[$ $(i,k=1,2)$ are continuous functions. The optimal, in a certain sense, sufficient conditions are obtained for the existence and uniqueness of a nonnegative solution of the problem (1.1), (1.2).http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1 |
| spellingShingle | Ivan Kiguradze Nino Partsvania On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments Electronic Journal of Qualitative Theory of Differential Equations |
| title | On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments |
| title_full | On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments |
| title_fullStr | On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments |
| title_full_unstemmed | On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments |
| title_short | On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments |
| title_sort | on nonnegative solutions of nonlinear two point boundary value problems for two dimensional differential systems with advanced arguments |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1 |
| work_keys_str_mv | AT ivankiguradze onnonnegativesolutionsofnonlineartwopointboundaryvalueproblemsfortwodimensionaldifferentialsystemswithadvancedarguments AT ninopartsvania onnonnegativesolutionsofnonlineartwopointboundaryvalueproblemsfortwodimensionaldifferentialsystemswithadvancedarguments |