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

Abstract

Let Ω be a bounded open interval, let p>1${p>1}$ and γ>0${\gamma>0}$, and let m:Ω→ℝ${m:\Omega\rightarrow\mathbb{R}}$ 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 -(|u′|p-2⁢u′)′=m⁢(x)⁢u-γ${-(|u^{\prime}|^{p-2}u^{\prime})^{\prime}=m(x)u^{-\gamma}}$ in Ω, u=0${u=0}$ on ∂⁡Ω${\partial\Omega}$. As a consequence we also derive existence results for other related nonlinearities.

Keywords

• one-dimensional singular problems
• indefinite nonlinearities
• positive solutions
• 34b16
• 34b18
• 34b15
• 34c25