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The boundary-value problem on semi-axis for one class operator-differentialequations of the fourth order, the main part of which has the multiplecharacteristic is investigated in this paper in Sobolev type weighted space.Correctness and unique solvability of the boundary-value problem is proved, andthe solvability conditions are expressed in terms of the operator coefficientsof the equation. Estimations of the norms of the operators of intermediatederivatives, closely connected with the solvability conditions, have beencarried out. The connection between the exponent of the weight and the lowerborder of the spectrum of the main operator, participating in the equation, isdetermined in the results of the paper.

On a Boundary-Value Problem for One Class of Differential Equations of the Fourth Order with Operator Coefficients