## Differential and Integral Equations

### A singular Sturm-Liouville equation under non-homogeneous boundary conditions

#### Abstract

Given $\alpha > 0$ and $f\in L^2(0,1)$, consider the following singular Sturm-Liouville equation: \left\lbrace\begin{aligned} -(x^{2\alpha}u'(x))'+u(x) & =f(x) \ \hbox{ a.e. on } (0,1),\\ u(1) & =0. \end{aligned}\right. We prove existence of solutions under (weighted) non-homogeneous boundary conditions at the origin.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 1/2 (2012), 85-92.

Dates
First available in Project Euclid: 20 December 2012