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

• Published in: Boundary value problems Vol. 2012; no. 1; p. 40
• Main Author: Hormozi, Mahdi
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2012; BioMed Central Ltd
• Subjects: Analysis; Approximations and Expansions; boundary condition; Difference and Functional Equations; Matematisk analys; Mathematical Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Prufer transformation; Sturm–Liouville equation; boundary condition; Prüfer transformation; Sturm-Liouville equation
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/1687-2770-2012-40

In this article, we derive an asymptotic approximation to the eigenvalues of the linear differential equation - y ″ ( x ) + q ( x ) y ( x ) = λ y ( x ) , x ∈ ( a , b ) 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.