Positive solutions of second-order three-point boundary value problems with sign-changing coefficients
In this article, we investigate the boundary-value problem \begin{equation*} \begin{cases}x''(t)+h(t)f(x(t))=0,\quad t\in[0,1],\\ x(0)=\beta x'(0),\quad x(1)=x(\eta),\end{cases} \end{equation*} where $\beta\ge0$, $\eta\in(0,1)$, $f\in C([0,\infty), [0,\infty))$ is nondecreasing, a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2016-10-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5158 |
| _version_ | 1797830599283572736 |
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| author | Ye Xue Guowei Zhang |
| author_facet | Ye Xue Guowei Zhang |
| author_sort | Ye Xue |
| collection | DOAJ |
| description | In this article, we investigate the boundary-value problem
\begin{equation*}
\begin{cases}x''(t)+h(t)f(x(t))=0,\quad t\in[0,1],\\
x(0)=\beta x'(0),\quad x(1)=x(\eta),\end{cases}
\end{equation*}
where $\beta\ge0$, $\eta\in(0,1)$, $f\in C([0,\infty), [0,\infty))$ is nondecreasing, and importantly $h$ changes sign on $[0,1]$. By the Guo-Krasnosel'skii fixed-point theorem in a cone, the existence of positive solutions is obtained via a special cone in terms of superlinear or sublinear behavior of $f$. |
| first_indexed | 2024-04-09T13:38:41Z |
| format | Article |
| id | doaj.art-b82cdf2e17b5403e86c86d53437074f9 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:41Z |
| publishDate | 2016-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-b82cdf2e17b5403e86c86d53437074f92023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-10-0120169711010.14232/ejqtde.2016.1.975158Positive solutions of second-order three-point boundary value problems with sign-changing coefficientsYe Xue0Guowei Zhang1Department of Mathematics, Northeastern University, Shenyang 110819, ChinaNortheastern University, Shenyang, P. R. ChinaIn this article, we investigate the boundary-value problem \begin{equation*} \begin{cases}x''(t)+h(t)f(x(t))=0,\quad t\in[0,1],\\ x(0)=\beta x'(0),\quad x(1)=x(\eta),\end{cases} \end{equation*} where $\beta\ge0$, $\eta\in(0,1)$, $f\in C([0,\infty), [0,\infty))$ is nondecreasing, and importantly $h$ changes sign on $[0,1]$. By the Guo-Krasnosel'skii fixed-point theorem in a cone, the existence of positive solutions is obtained via a special cone in terms of superlinear or sublinear behavior of $f$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5158positive solutionfixed point theoremconesign-changing coefficient |
| spellingShingle | Ye Xue Guowei Zhang Positive solutions of second-order three-point boundary value problems with sign-changing coefficients Electronic Journal of Qualitative Theory of Differential Equations positive solution fixed point theorem cone sign-changing coefficient |
| title | Positive solutions of second-order three-point boundary value problems with sign-changing coefficients |
| title_full | Positive solutions of second-order three-point boundary value problems with sign-changing coefficients |
| title_fullStr | Positive solutions of second-order three-point boundary value problems with sign-changing coefficients |
| title_full_unstemmed | Positive solutions of second-order three-point boundary value problems with sign-changing coefficients |
| title_short | Positive solutions of second-order three-point boundary value problems with sign-changing coefficients |
| title_sort | positive solutions of second order three point boundary value problems with sign changing coefficients |
| topic | positive solution fixed point theorem cone sign-changing coefficient |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5158 |
| work_keys_str_mv | AT yexue positivesolutionsofsecondorderthreepointboundaryvalueproblemswithsignchangingcoefficients AT guoweizhang positivesolutionsofsecondorderthreepointboundaryvalueproblemswithsignchangingcoefficients |