Abstract
In this paper we consider perturbations of a second order differential equation of the spectral problem with a loaded term, containing a value of the unknown function at the point zero, with regular, but not strongly regular boundary value conditions. Question about basis property of eigen functions and associated functions (E&AF) systems of a loaded multiple differentiation operator is studied. In the case of non-self-adjoint ordinary differential operators, the basis property of systems of eigen functions and associated functions (E&AF), in addition to the boundary value conditions, can be affected by values of coefficients of the differential operator. Moreover, it is known that the basic properties of E&AF can be changed at a small change of values of the coefficients. This fact was first noted in Il’in V.A. In this paper problem non stability on basis property of systems root vectors of a loaded multiple differentiation operator.