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\...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2019-01, Vol.2019 (90), p.1-13
Main Authors: Hai, Dang Dinh, Wang, Xiao
Format: Article
Language:English
Subjects:
integral boundary conditions
p$-laplacian
positive solutions
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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 $u=0.$
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2019.1.90