Geodesic
Distribution of the eigenvalues of singular differential operators in a space of vector-functions
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 107-123

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A significant part of B. M. Levitan's scientific activity dealt with questions on the distribution of the eigenvalues of differential operators [1]. To study the spectral density, he mainly used Carleman's method, which he perfected. As a rule, he considered scalar differential operators. The purpose of this paper is to study the spectral density of differential operators in a space of vector-functions. The paper consists of two sections. In the first we study the asymptotics of a fourth-order differential operator $$ y^{(4)}+Q(x)y=\lambda y, $$ both taking account of the rotational velocity of the eigenvectors of the matrix $ Q(x)$ and without taking the rotational velocity of these vectors into account. In Section 2 we study the asymptotics of the spectrum of a non-semi-bounded Sturm–Liouville operator in a space of vector-functions of any finite dimension. 
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     title = {Distribution of the eigenvalues of singular differential operators in a space of vector-functions},
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N. F. Valeev; È. A. Nazirova; Ya. T. Sultanaev. Distribution of the eigenvalues of singular differential operators in a space of vector-functions. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 107-123. http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a1/