Аннотация
The present paper is devoted to the study of the abstract nonlocal boundary value problem with integral type Samarskii–Ionkin conditions for the differential equation of elliptic type \[\hspace{-6em} -u''(t)+Au(t)=f(t)\quad (0\leq t\leq T),\quad u\left( 0\right) =\varphi,\quad u'\left( 0\right) =u'\left( T\right) +\int\limits_{0}^{T}\alpha \left( s\right) u(s)ds+\psi.\quad\] in an arbitrary Banach space \(E\) with the positive operator \(A\). The well-posedness of this problem in various Banach spaces is established. In applications, theorems on the well-posedness of several nonlocal boundary value problems for elliptic equations with integral type Samarskii–Ionkin conditions are proved.