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STRICTLY POSITIVE SOLUTIONS FOR ONE-DIMENSIONAL NONLINEAR PROBLEMS INVOLVING THE
$p$-LAPLACIAN
Published online by Cambridge University Press: 06 September 2013
Abstract
Let $\Omega $ be a bounded open interval, and let
$p\gt 1$ and
$q\in (0, p- 1)$. Let
$m\in {L}^{{p}^{\prime } } (\Omega )$ and
$0\leq c\in {L}^{\infty } (\Omega )$. We study the existence of strictly positive solutions for elliptic problems of the form
$- (\vert {u}^{\prime } \mathop{\vert }\nolimits ^{p- 2} {u}^{\prime } ){\text{} }^{\prime } + c(x){u}^{p- 1} = m(x){u}^{q} $ in
$\Omega $,
$u= 0$ on
$\partial \Omega $. We mention that our results are new even in the case
$c\equiv 0$.
Keywords
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- Research Article
- Information
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
References
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