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

preprint2012arXivOpen access

Abstract

In this paper, we derive an asymptotic approximation to the eigenvalues of the linear differential equation −y"(x)+q(x)y(x)=λy(x),x∈(a,b) -y"(x)+q(x)y(x)=λy(x), x\in (a,b) with boundary conditions of general form, when qq is a measurable function which has a singularity in (a,b)(a,b) and which is integrable on subsets of (a,b)(a,b) which exclude the singularity.

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