Spectral properties of a fourth-order differential operator with integrable coefficients

Proceedings of the Steklov Institute of Mathematics (Impact Factor: 0.3). 09/2010; 270(1):184-193. DOI: 10.1134/S0081543810030144


The aim of this paper is to study spectral properties of differential operators with integrable coefficients and a constant
weight function. We analyze the asymptotic behavior of solutions to a differential equation with integrable coefficients for
large values of the spectral parameter. To find the asymptotic behavior of solutions, we reduce the differential equation
to a Volterra integral equation. We also obtain asymptotic formulas for the eigenvalues of some boundary value problems related
to the differential operator under consideration.

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