A note on the NBVP with Samarskii-Ionkin condition I for elliptic equations

In the present paper, the nonlocal boundary value problem with Samarskii-Ionkin condition I for elliptic equations in a Banach space with the positive operator is investigated. The main theorems on well-posedness of this problem are established. In practice, the coercive stability estimates for solution of four types of nonlocal boundary value problems with Samarskii-Ionkin condition I for elliptic differential equations are proved. © 2025, Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan. All rights reserved.