About the spectral properties of the family of the differential operator of even order with summable potential

The article is devoted to investigating the method for studying the spectral properties of differential operators of high even order with summable potential. The asymptotic behavior of the solutions of the corresponding differential equation has been found for large values of the spectral parameter. The boundary conditions have been studied, and the equation for eigenvalues of the operator under investigation has been formulated. The indicator diagram of this equation has been studied. The asymptotic behavior of eigenvalues of the studied operator has been found.