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

Proceedings of the Steklov Institute of Mathematics (impact factor: 0.17). 05/2012; 270(1):184-193. DOI:10.1134/S0081543810030144 pp.184-193

ABSTRACT 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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### Keywords

asymptotic behavior

asymptotic formulas

boundary value problems

differential equation

differential operator

differential operators

eigenvalues

integrable coefficients

large values

study spectral properties

Volterra integral equation