A singular nonlinear boundary value problem with Neumann conditions

Abstract

We study the existence of solutions for the equations $x^{\prime\prime}\pm g(t,x)=h(t)$, $t\in (0,1)$ with Neumann boundary conditions, where $g:[0,1] \times (0,+\infty) \to [0,+\infty)$ and $h:[0,1] \to \mathbb{R}$ are continuous and $g(t,\cdot)$ is singular at $0$ for each $t\in [0,1]$.