Geodesic
Spectral properties of a~fourth-order differential operator with integrable coefficients
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 188-197

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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. 
@article{TM_2010_270_a13,
     author = {S. I. Mitrokhin},
     title = {Spectral properties of a~fourth-order differential operator with integrable coefficients},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {188--197},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a13/}
}
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S. I. Mitrokhin. Spectral properties of a~fourth-order differential operator with integrable coefficients. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 188-197. http://geodesic.mathdoc.fr/item/TM_2010_270_a13/