In this work some boundary value problem for the operator-differential equations of the second order of elliptic type is investigated on a finite segment. Here sufficient conditions are specified operator coefficients of the equation, at which boundary value regularly or fredholm's solvability. The received results are applied to some boundary value for differential the equations of the second order in private derivatives of elliptic type.

Regular solvability of one boundary value problem for the operator differential equations in abstract Hilbert spaces is investigated in this paper. Sufficient conditions for the coefficients of the operator differential equation, which provide the regular solvability for this problem, are found. The results of this work are applied to some mixed problems for the second order elliptic type equation with partial derivatives.