One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign

Let $Ω$ be a bounded open interval, let $p>1$ and $γ>0$, and let $m:Ω\rightarrow\mathbb{R}$ be a function that may change sign in $Ω$. In this article we study the existence and nonexistence of positive solutions for one-dimensional singular problems of the form $-(\left\vert u^{\prime}\right\vert ^{p-2}u^{\prime})^{\prime}=m\left( x\right) u^{-γ}$ in $Ω$, $u=0$ on $\partialΩ$. As a consequence we also derive existence results for other related nonlinearities.

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