On the stability and instability of the basis properties of root functions of the Schrödinger equation with nonlocal perturbations of boundary condition

Abstract

In paper Samarsky-Ionkin spectral problem for the Schrodinger equation with an integral perturbation in the boundary conditions is considered. It is assumed that the unperturbed problem has a system of eigenfunctions forming Riesz basis in L2 (0,1). It is shown that the basis property of the systems of root functions of a prob¬lem can be varied under any arbitrarily small variation of the kernel of the integral perturbation.