Differential and Integral Equations

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

Hernán Castro and Hui Wang

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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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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