Distribution of the eigenvalues of the Sturm–Liouville operator equation

V. A. Mikhailets


Abstract: This work contains an analysis of the dependence of the lower terms of the asymptotics of the distribution of the eigenvalues of the equation $-y''+Ay=\lambda y$ upon the spectrum of the positive selfadjoint operator $A$ and the form of the boundary conditions. As a corollary the second term is found for the spectral asymptotics of classical boundary value problems for the Laplace equation in three-dimensional cylindrical domains.
Bibliography: 20 titles.

UDC: 517.9

MSC: Primary 34B25, 34G05, 47A50; Secondary 47B25, 35A15, 35J05

Received: 06.05.1976

 English version: Mathematics of the USSR-Izvestiya, 1977, 11:3, 571–582

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