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STRICTLY POSITIVE SOLUTIONS FOR ONE-DIMENSIONAL NONLINEAR PROBLEMS INVOLVING THE
$p$-LAPLACIAN
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 2 / April 2014
- Published online by Cambridge University Press:
- 06 September 2013, pp. 243-251
- Print publication:
- April 2014
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- Article
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- You have access
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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 
$c\equiv 0$.
