Existence of positive solutions for singular p-Laplacian Sturm-Liouville boundary value problems

We prove the existence of positive solutions of the Sturm-Liouville boundary value problem $$\displaylines{ -(r(t)\phi (u'))'=\lambda g(t)f(t,u),\quad t\in (0,1),\cr au(0)-b\phi ^{-1}(r(0))u'(0)=0,\quad cu(1)+d\phi ^{-1}(r(1))u'(1)=0, }$$ where $\phi (u')=|u'|^{p-2}u�...

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Bibliographic Details
Published in:Electronic journal of differential equations 2016-09, Vol.2016 (260), p.1-9
Main Author: D. D. Hai
Format: Article
Language:English
Subjects:
positive solution
Singular Sturm-Liouville boundary value problem
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Summary:We prove the existence of positive solutions of the Sturm-Liouville boundary value problem $$\displaylines{ -(r(t)\phi (u'))'=\lambda g(t)f(t,u),\quad t\in (0,1),\cr au(0)-b\phi ^{-1}(r(0))u'(0)=0,\quad cu(1)+d\phi ^{-1}(r(1))u'(1)=0, }$$ where $\phi (u')=|u'|^{p-2}u'$, $p>1$, $f:(0,1)\times(0,\infty )\to \mathbb{R}$ satisfies a p-sublinear condition and is allowed to be singular at u=0 with semipositone structure. Our results extend previously known results in the literature.
ISSN:1072-6691