Article

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
 

S. I. Mitrokhin