IJPAM: Volume 82, No. 2 (2013)
THE REGULAR STURM-LIOUVILLE OPERATOR
Department of Mathematical Sciences
Tennessee State University
3500, John A Merritt Blvd.
Nashville, TN, 37209, USA
Abstract. It is known that the minimum and minimizer of the Rayleigh quotient provide the eigenvalues and eigenfunctions of a regular Srurm-Liouville operator. This expository paper uses elementary calculus method and some of the fundamental theorems of functional analysis, namely Arzela Ascoli's theorem and Lax-Milgram theorem to show the same result.
Received: October 27, 2012
AMS Subject Classification: 34B09, 34L15
Key Words and Phrases: eigenfunctions, eigenvalues, Sturm-Liouville BVP, Rayleigh quotient
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395