TY - JOUR
AU - Baranetskij, Ya.O.
AU - Kalenyuk, P.I.
AU - Kopach, M.I.
AU - Solomko, A.V.
PY - 2020/06/28
Y2 - 2024/11/09
TI - The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. II
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 12
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.12.1.173-188
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/3902
SP - 173-188
AB - <p>In this paper we continue to investigate the properties of the problem with nonlocal conditions, which are multipoint perturbations of mixed boundary conditions, started in the first part. In particular, we construct a generalized transform operator, which maps the solutions of the self-adjoint boundary-value problem with mixed boundary conditions to the solutions of the investigated multipoint problem. The system of root functions $V(L)$ of operator $L$ for multipoint problem is constructed. The conditions under which the system $V(L)$ is complete and minimal, and the conditions under which it is the Riesz basis are determined. In the case of an elliptic equation the conditions of existence and uniqueness of the solution for the problem are established.</p>
ER -