FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 6, PAGES 137-155

On the number of real eigenvalues of a certain boundary-value problem for a second-order equation with fractional derivative

A. Yu. Popov

Abstract

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The asymptotics as a → 0+ of the number of real eigenvalues ln(a) of the problem y''(x) + lD0ay(x) = 0, 0 < x < 1, y(0) = y(1) = 0, is found. The minimization of real eigenvalues was carried out. It is proved that lima → 0+ ln(a) = (pn)2.

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