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 |
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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 |
| Summary: | 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 $u=0.$ |
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| ISSN: | 1417-3875 1417-3875 |