On a study of the spectrum of a boundary value problem for the fifth-order differential operator with integrable potential

A boundary value problem for the fifth-order differential operator with separated boundary conditions is considered. The potential of the operator is a summable function on the segment. For large values of the spectral parameter we obtain the asymptotic behavior of the corresponding differential equation. The equation on eigenvalues of the considered operator and the indicator diagram of this equation are studied. A new method for finding an asymptotics of eigenvalues of the studied operator is offered.