Differential and Integral Equations

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

Hernán Castro and Hui Wang

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012827

Mathematical Reviews number (MathSciNet)
MR2906548

Zentralblatt MATH identifier
1249.34065

Subjects
Primary: 34B08: Parameter dependent boundary value problems 34B05: Linear boundary value problems

Citation

Castro, Hernán; Wang, Hui. A singular Sturm-Liouville equation under non-homogeneous boundary conditions. Differential Integral Equations 25 (2012), no. 1/2, 85--92. https://projecteuclid.org/euclid.die/1356012827


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