On singular $p$-Laplacian boundary value problems involving integral boundary conditions
We prove the existence of positive solutions for the $p$-Laplacian equations \[-(\phi (u^{\prime }))^{\prime }=\lambda f(t,u),\qquad t\in (0,1) \] with integral boundary conditions. Here $\lambda $ is a positive parameter, $\phi (s)=|s|^{p-2}s,p>1,\ f:(0,1)\times (0,\infty )\rightarrow \mathbb{R\...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-12-01
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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=7389 |
| _version_ | 1797830490784268288 |
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| author | Dang Dinh Hai Xiao Wang |
| author_facet | Dang Dinh Hai Xiao Wang |
| author_sort | Dang Dinh Hai |
| collection | DOAJ |
| description | We prove the existence of positive solutions for the $p$-Laplacian equations
\[-(\phi (u^{\prime }))^{\prime }=\lambda f(t,u),\qquad t\in (0,1) \]
with integral boundary conditions. Here $\lambda $ is a positive parameter, $\phi (s)=|s|^{p-2}s,p>1,\ f:(0,1)\times (0,\infty )\rightarrow \mathbb{R\ }$ is $p$-superlinear or $p$-sublinear at $\infty $ and is allowed be singular at $t=0,1$ and $u=0.$ |
| first_indexed | 2024-04-09T13:36:57Z |
| format | Article |
| id | doaj.art-1c70c3c118834e8eba3a55fc3f6df0d8 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:57Z |
| publishDate | 2019-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1c70c3c118834e8eba3a55fc3f6df0d82023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-12-0120199011310.14232/ejqtde.2019.1.907389On singular $p$-Laplacian boundary value problems involving integral boundary conditionsDang Dinh Hai0Xiao Wang1Mississippi State University, Mississippi State, USAMississippi State University, Mississippi State, USAWe prove the existence of positive solutions for the $p$-Laplacian equations \[-(\phi (u^{\prime }))^{\prime }=\lambda f(t,u),\qquad t\in (0,1) \] with integral boundary conditions. Here $\lambda $ is a positive parameter, $\phi (s)=|s|^{p-2}s,p>1,\ f:(0,1)\times (0,\infty )\rightarrow \mathbb{R\ }$ is $p$-superlinear or $p$-sublinear at $\infty $ and is allowed be singular at $t=0,1$ and $u=0.$http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7389$p$-laplacianintegral boundary conditionspositive solutions |
| spellingShingle | Dang Dinh Hai Xiao Wang On singular $p$-Laplacian boundary value problems involving integral boundary conditions Electronic Journal of Qualitative Theory of Differential Equations $p$-laplacian integral boundary conditions positive solutions |
| title | On singular $p$-Laplacian boundary value problems involving integral boundary conditions |
| title_full | On singular $p$-Laplacian boundary value problems involving integral boundary conditions |
| title_fullStr | On singular $p$-Laplacian boundary value problems involving integral boundary conditions |
| title_full_unstemmed | On singular $p$-Laplacian boundary value problems involving integral boundary conditions |
| title_short | On singular $p$-Laplacian boundary value problems involving integral boundary conditions |
| title_sort | on singular p laplacian boundary value problems involving integral boundary conditions |
| topic | $p$-laplacian integral boundary conditions positive solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7389 |
| work_keys_str_mv | AT dangdinhhai onsingularplaplacianboundaryvalueproblemsinvolvingintegralboundaryconditions AT xiaowang onsingularplaplacianboundaryvalueproblemsinvolvingintegralboundaryconditions |