On the Solvability of the Boundary-Value Problem for Second-Order Equations in Hilbert Space with an Operator Coefficient in the Boundary Condition

We consider the boundary-value problem on a finite interval for a class of second-order operator-differential equations with a linear operator in one of its boundary conditions. We obtain sufficient conditions for the regular solvability of the boundary-value problem under consideration; these conditions are expressed only in terms of its operator coefficients.