On a Boundary Value Problem for Fourth-Order Operator-Differential Equations with a Variable Coefficient

摘要

In this work, conditions for the regular solvability of one boundary-value problem for fourth-order operator-differential equations with a variable coefficient on the semi-axis are found. The obtained conditions are expressed by the properties of the coefficients of the considered operator-differential equation. Moreover, the norms of intermediate derivatives operators are estimated in terms of the norm of the right-hand side of the equation and these estimates are related to the solvability conditions of the boundary value problem.