A problem for a factorized equation with a pseudoparabolic differential operator

A new problem is proposed for a fourth-order factorized differential equation whose operator is the product of a first- and third-order differential operator. The existence and uniqueness of the solution of the problem are proved. The solution is constructed in terms of the Riemann function of the corresponding pseudoparabolic differential operator of the third order, and one of the functions included in the formula for solving the problem is determined in the resolvents of two integral equations.