Characteristic determinant of a perturbed regular third-order differential operator on an interval

In the paper, we consider the spectral problem for a third-order operator with an integral perturbation of one of the boundary value conditions that are regular and at the same time strongly regular; a feature of the problem is that the conjugate operator will be a loaded third-order differential operator with regular (strongly regular) boundary value conditions. Moreover, a characteristic determinant of the spectral problem is constructed, on the basis of which conclusions about eigenvalues of the perturbed operator are assumed.