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

• Main Authors: Kaufmann Uriel, Medri Iván
• Format: Article
• Language: English
• Published: De Gruyter 2016-08-01
• Series: Advances in Nonlinear Analysis
• Subjects: one-dimensional singular problems; indefinite nonlinearities; positive solutions; 34b16; 34b18; 34b15; 34c25
• Online Access: https://doi.org/10.1515/anona-2015-0116

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.