Generalized Samarsky–Ionkin problem for Sobolev-type equations of odd order

The work is investigating the solvability of nonlocal problems with the generalized Samarskii–Ionkin boundary condition for a special class of Sobolev-type equations, namely, for the so-called pseudoparabolic equations. We prove the existence and uniqueness theorems for regular solutions to the problems, i.e., for the solutions that have all generalized by Sobolev derivatives included in the corresponding equations. Moreover, some improvements and generalizations of the obtained results are described.

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