@article{Baranetskij_Kalenyuk_Kopach_Solomko_2019, title={The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. I: Array}, volume={11}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/2103}, DOI={10.15330/cmp.11.2.228-239}, abstractNote={<p>In this article we investigate a problem with nonlocal boundary conditions which are multipoint perturbations of mixed boundary conditions in the unit square $G$ using the Fourier method. The properties of a generalized transformation operator $R: L_2(G) \to L_2(G)$ that reflects normalized eigenfunctions of the operator $L_0$ of the problem with mixed boundary conditions in the eigenfunctions of the operator $L$ for nonlocal problem with perturbations, are studied. We construct a system $V(L)$ of eigenfunctions of operator $L.$ Also, we define conditions under which the system $V(L)$ is total and minimal in the space $L_{2}(G),$ and conditions under which it is a Riesz basis in the space $L_{2}(G).$ In the case if $V(L)$ is a Riesz basis in $L_{2}(G),$ we obtain sufficient conditions under which nonlocal problem has a unique solution in form of Fourier series by system $V(L).$</p>}, number={2}, journal={Carpathian Mathematical Publications}, author={Baranetskij, Ya.O. and Kalenyuk, P.I. and Kopach, M.I. and Solomko, A.V.}, year={2019}, month={Dec.}, pages={228–239} }