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. [ABSTRACT FROM AUTHOR]