Electron. J. Differential Equations, Vol. 2016 (2016), No. 260, pp. 1-9.

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

D. D. Hai

Abstract:
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.

Submitted May 20, 2016. Published September 26, 2016.
Math Subject Classifications: 34B16, 34B18.
Key Words: Singular Sturm-Liouville boundary value problem; positive solution.

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Hai Dinh Dang
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
email: dang@math.msstate.edu

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