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 $$a → 0+ of the number of real eigenvalues $$l_n(a) of the problem $y\text{'}\text{'}(x)\; +$lD₀^ay(x) = 0, , $y(0)\; =\; y(1)\; =\; 0$, is found. The minimization of real eigenvalues was carried out. It is proved that $lim$_{a → 0+} l_n(a) = (pn)².

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Last modified: February 26, 2007