Spatial-nonlocal boundary value problems with the generalized Samarskyii-Ionkin condition for some classes of non-stationary differential equations

The problem, to which this paper is devoted, apparently appeared for the first time in mathematical physics 125 years ago in the work of V. A. Steklov. The modern stage in her research began in 1977; in modern literature, especially foreign literature, this problem is called the Samarskii-Ionkin problem.
The report presents new results, which significantly strengthen the known ones, on the solvability of the generalized Samarskii-Ionkin problem in classes of regular solutions for parabolic, ultra-parabolic, pseudo-parabolic and other differential equations.