Composite-type differential equations with degeneration

The paper is devoted to the study of the solvability of boundary value problems for fourth-order linear composite-type differential equations. A distinctive feature of the considered equations is that the operator coefficient at the highest derivative with respect to the time (distinguished) variable may be non-invertible. For the problems under study, theorems on the existence and uniqueness of regular solutions are proved—solutions that possess all generalized derivatives in the sense of S.L. Sobolev entering the corresponding equation.