Existence of positive solutions for boundary value problem of second-order functional differential equation
We use a fixed point index theorem in cones to study the existence of positive solutions for boundary value problems of second-order functional differential equations of the form $$\left\{ \begin{array}{ll} y''(x)+r(x)f(y(w(x)))=0,&0<x<1,\\ \alpha y(x)-\beta y'(x)=\xi (x),&a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
1998-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11 |
| _version_ | 1797830808566759424 |
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| author | Daqing Jiang P. Weng |
| author_facet | Daqing Jiang P. Weng |
| author_sort | Daqing Jiang |
| collection | DOAJ |
| description | We use a fixed point index theorem in cones to study the existence of positive solutions for boundary value problems of second-order functional differential equations of the form $$\left\{ \begin{array}{ll} y''(x)+r(x)f(y(w(x)))=0,&0<x<1,\\ \alpha y(x)-\beta y'(x)=\xi (x),&a\leq x\leq 0,\\ \gamma y(x)+\delta y'(x)=\eta (x),&1\leq x\leq b; \end{array}\right.$$ where $w(x)$ is a continuous function defined on $[0,1]$ and $r(x)$ is allowed to have singularities on $[0,1]$. The result here is the generalization of a corresponding result for ordinary differential equations. |
| first_indexed | 2024-04-09T13:42:00Z |
| format | Article |
| id | doaj.art-d4ddf7ee903247c681ec4be572b9048c |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:42:00Z |
| publishDate | 1998-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-d4ddf7ee903247c681ec4be572b9048c2023-05-09T07:52:56ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751998-01-011998611310.14232/ejqtde.1998.1.611Existence of positive solutions for boundary value problem of second-order functional differential equationDaqing Jiang0P. Weng1Northeast Normal University, Changchun, P. R. ChinaSouth China Normal University, Guangzhou, P. R. ChinaWe use a fixed point index theorem in cones to study the existence of positive solutions for boundary value problems of second-order functional differential equations of the form $$\left\{ \begin{array}{ll} y''(x)+r(x)f(y(w(x)))=0,&0<x<1,\\ \alpha y(x)-\beta y'(x)=\xi (x),&a\leq x\leq 0,\\ \gamma y(x)+\delta y'(x)=\eta (x),&1\leq x\leq b; \end{array}\right.$$ where $w(x)$ is a continuous function defined on $[0,1]$ and $r(x)$ is allowed to have singularities on $[0,1]$. The result here is the generalization of a corresponding result for ordinary differential equations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11 |
| spellingShingle | Daqing Jiang P. Weng Existence of positive solutions for boundary value problem of second-order functional differential equation Electronic Journal of Qualitative Theory of Differential Equations |
| title | Existence of positive solutions for boundary value problem of second-order functional differential equation |
| title_full | Existence of positive solutions for boundary value problem of second-order functional differential equation |
| title_fullStr | Existence of positive solutions for boundary value problem of second-order functional differential equation |
| title_full_unstemmed | Existence of positive solutions for boundary value problem of second-order functional differential equation |
| title_short | Existence of positive solutions for boundary value problem of second-order functional differential equation |
| title_sort | existence of positive solutions for boundary value problem of second order functional differential equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11 |
| work_keys_str_mv | AT daqingjiang existenceofpositivesolutionsforboundaryvalueproblemofsecondorderfunctionaldifferentialequation AT pweng existenceofpositivesolutionsforboundaryvalueproblemofsecondorderfunctionaldifferentialequation |