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arXiv · 1307.1817

Strictly positive solutions for one-dimensional nonlinear problems involving the p-Laplacian

Uriel Kaufmann·Ivan Medri
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Abstract

Let $Ω$ be a bounded open interval, and let $p>1$ and $q\in\left(0,p-1\right) $. Let $m\in L^{p^{\prime}}\left(Ω\right) $ and $0\leq c\in L^{\infty}\left(Ω\right) $. We study existence of strictly positive solutions for elliptic problems of the form $-\left(\left\| u^{\prime}\right\|^{p-2}u^{\prime}\right) ^{\prime}+c\left(x\right) u^{p-1}=m\left(x\right) u^{q}$ in $Ω$, $u=0$ on $\partialΩ$. We mention that our results are new even in the case $c\equiv0$.

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Uriel Kaufmann, Ivan Medri. 2013-07-06. Strictly positive solutions for one-dimensional nonlinear problems involving the p-Laplacian. https://doi.org/10.1017/s0004972713000725

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