Differentiation of solutions of nonlocal boundary value problems with respect to boundary data
In this paper, we investigate boundary data smoothness for solutions of the nonlocal boundary value problem, $y^{(n)}=f(x,y,y',\ldots,y^{(n-1)}),y^{(i)}(x_j)=y_{ij}$ and $y^{(i)}(x_k)-\sum_{p=1}^m r_{ip}y(\eta_{ip})=y_{ik}.$ Essentially, we show under certain conditions that partial derivatives...
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| Format: | Article |
| Language: | English |
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University of Szeged
2011-07-01
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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=713 |
| _version_ | 1797830722605547520 |
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| author | Jeffrey Lyons |
| author_facet | Jeffrey Lyons |
| author_sort | Jeffrey Lyons |
| collection | DOAJ |
| description | In this paper, we investigate boundary data smoothness for solutions of the nonlocal boundary value problem, $y^{(n)}=f(x,y,y',\ldots,y^{(n-1)}),y^{(i)}(x_j)=y_{ij}$ and $y^{(i)}(x_k)-\sum_{p=1}^m r_{ip}y(\eta_{ip})=y_{ik}.$ Essentially, we show under certain conditions that partial derivatives of the solution to the problem above exist with respect to boundary conditions and solve the associated variational equation. Lastly, we provide a corollary and nontrivial example. |
| first_indexed | 2024-04-09T13:40:38Z |
| format | Article |
| id | doaj.art-826665b625e1494d8cf6278d0b19e102 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:38Z |
| publishDate | 2011-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-826665b625e1494d8cf6278d0b19e1022023-05-09T07:53:01ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752011-07-0120115111110.14232/ejqtde.2011.1.51713Differentiation of solutions of nonlocal boundary value problems with respect to boundary dataJeffrey Lyons0Texas A&M University, Corpus Christi, TX, U.S.A.In this paper, we investigate boundary data smoothness for solutions of the nonlocal boundary value problem, $y^{(n)}=f(x,y,y',\ldots,y^{(n-1)}),y^{(i)}(x_j)=y_{ij}$ and $y^{(i)}(x_k)-\sum_{p=1}^m r_{ip}y(\eta_{ip})=y_{ik}.$ Essentially, we show under certain conditions that partial derivatives of the solution to the problem above exist with respect to boundary conditions and solve the associated variational equation. Lastly, we provide a corollary and nontrivial example.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=713nonlinear boundary value problemvariational equationordinary differential equationnonlocal boundary conditionuniquenessexistence |
| spellingShingle | Jeffrey Lyons Differentiation of solutions of nonlocal boundary value problems with respect to boundary data Electronic Journal of Qualitative Theory of Differential Equations nonlinear boundary value problem variational equation ordinary differential equation nonlocal boundary condition uniqueness existence |
| title | Differentiation of solutions of nonlocal boundary value problems with respect to boundary data |
| title_full | Differentiation of solutions of nonlocal boundary value problems with respect to boundary data |
| title_fullStr | Differentiation of solutions of nonlocal boundary value problems with respect to boundary data |
| title_full_unstemmed | Differentiation of solutions of nonlocal boundary value problems with respect to boundary data |
| title_short | Differentiation of solutions of nonlocal boundary value problems with respect to boundary data |
| title_sort | differentiation of solutions of nonlocal boundary value problems with respect to boundary data |
| topic | nonlinear boundary value problem variational equation ordinary differential equation nonlocal boundary condition uniqueness existence |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=713 |
| work_keys_str_mv | AT jeffreylyons differentiationofsolutionsofnonlocalboundaryvalueproblemswithrespecttoboundarydata |