SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Open Badges Research

A note on a paper of Harris concerning the asymptotic approximation to the eigenvalues of -y'' + qy = λy, with boundary conditions of general form

Mahdi Hormozi

Author affiliations

Department of Mathematical Sciences, Division of Mathematics, Chalmers University of Technology and University of Gothenburg, Gothenburg 41296, Sweden

Citation and License

Boundary Value Problems 2012, 2012:40  doi:10.1186/1687-2770-2012-40

Published: 12 April 2012


In this article, we derive an asymptotic approximation to the eigenvalues of the linear differential equation

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/40/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/40/mathml/M1">View MathML</a>

with boundary conditions of general form, when q is a measurable function which has a singularity in (a, b) and which is integrable on subsets of (a, b) which exclude the singularity.

Mathematics Subject Classification 2000: Primary, 41A05; 34B05; Secondary, 94A20.

Sturm-Liouville equation; boundary condition; Prüfer transformation.