Boundary value problems with an integro-differential non-local condition for composite type differential equations of the fourth order

The paper studies new nonlocal boundary value problems with an integro-differential boundary condition for unsteady differential equations of the Sobolev type of the fourth order. The peculiarity of the studied problems is that they contain derivatives both in spatial variables and derivatives in time variables in the boundary condition. For the problems under study, the existence and uniqueness theorems of regular solutions are proved – solutions having all derivatives generalized by S.L. Sobolev included in the corresponding equations.