Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions
We study the existence of positive solutions for some nonlinear second order boundary value problems with nonlocal boundary conditions. The key boundary condition considered is of the form $u(1)=\alpha[u']$, where $\alpha$ is a linear functional on $C[0,1]$, that is, is given by a Riemann-Stiel...
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-09-01
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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=5292 |
| _version_ | 1797830560062636032 |
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| author | Jeff Webb |
| author_facet | Jeff Webb |
| author_sort | Jeff Webb |
| collection | DOAJ |
| description | We study the existence of positive solutions for some nonlinear second order boundary value problems with nonlocal boundary conditions. The key boundary condition considered is of the form $u(1)=\alpha[u']$, where $\alpha$ is a linear functional on $C[0,1]$, that is, is given by a Riemann-Stieltjes integral $\alpha[v]=\int_0^1 v(s)dA(s)$ where $A$ is a function of bounded variation. It is important in our case that $dA$ is not a positive measure but can be sign changing. |
| first_indexed | 2024-04-09T13:38:01Z |
| format | Article |
| id | doaj.art-1d0b94184bdb4d32a1ddf6276a5e8889 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:01Z |
| publishDate | 2016-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1d0b94184bdb4d32a1ddf6276a5e88892023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-09-0120168611310.14232/ejqtde.2016.1.865292Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditionsJeff Webb0School of Mathematics and Statistics, University of Glasgow, Glasgow, UKWe study the existence of positive solutions for some nonlinear second order boundary value problems with nonlocal boundary conditions. The key boundary condition considered is of the form $u(1)=\alpha[u']$, where $\alpha$ is a linear functional on $C[0,1]$, that is, is given by a Riemann-Stieltjes integral $\alpha[v]=\int_0^1 v(s)dA(s)$ where $A$ is a function of bounded variation. It is important in our case that $dA$ is not a positive measure but can be sign changing.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5292fixed point indexnonlocal boundary condition |
| spellingShingle | Jeff Webb Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions Electronic Journal of Qualitative Theory of Differential Equations fixed point index nonlocal boundary condition |
| title | Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions |
| title_full | Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions |
| title_fullStr | Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions |
| title_full_unstemmed | Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions |
| title_short | Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions |
| title_sort | positive solutions of nonlinear differential equations with riemann stieltjes boundary conditions |
| topic | fixed point index nonlocal boundary condition |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5292 |
| work_keys_str_mv | AT jeffwebb positivesolutionsofnonlineardifferentialequationswithriemannstieltjesboundaryconditions |