Abstract
The asymptotics as α → 0+ of the number of real eigenvalues λ n (α) of the problem y″(x)+λD α0 (x) = 0, 0 < x < 1, y(0) = y(1) = 0, is obtained. The minimization of real eigenvalues is carried out. It is proved that \(\mathop {\lim }\limits_{\alpha \to 0 + } \lambda _n (\alpha ) = (\pi n)^2 \).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 137–155, 2006.
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Popov, A.Y. On the number of real eigenvalues of a certain boundary-value problem for a second-order equation with fractional derivative. J Math Sci 151, 2726–2740 (2008). https://doi.org/10.1007/s10948-008-0169-7
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DOI: https://doi.org/10.1007/s10948-008-0169-7