Spectral properties of the family of even order differential operators with a summable potential

A boundary value problem for a higher order differential operator with separated boundary conditions is considered. The asymptotics of solutions of the corresponding differential equation for large values of the spectral parameter is studied. The indicator diagram of the equation for the eigenvalues is studied. In various sector of the indicator diagram the asymptotic behavior of the eigenvalues and the formula for finding the eigenfunctions of the studied operator is obtained.