On the spectrum of the multipoint boundary value problem for an odd order differential operator with summable potential

A boundary value problem for an odd order differential operator with multipoint boundary conditions is studied. The interior points in which boundary conditions are set can divide the segment on which the operator is considered into the incommensurable parts. The potential of the differential operator is a function Lebesgue integrable at the segment on which the operator is considered. We study the asymptotic behaviour of the solutions to the corresponding differential equation for large values of the spectral parameter. The equation on the eigenvalues of the operator is received. We obtain the indicator diagram of that equation. The asymptotic behavior of the eigenvalues in all sectors of the indicator diagram is studied.