Strictly positive solutions for one-dimensional nonlinear problems involving the p-Laplacian
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 $c\equiv0$.
math.CA↗