A Problem for a Factorized Equation with a Pseudoparabolic Differential Operator.

We state a new problem for a fourth-order factorized differential equation, whose operator is the product of first- and third-order differential operators, and prove its unique solvability. We construct the solution in terms of the Riemann function of the corresponding third-order pseudoparabolic differential operator, determining one of functions that enter in the formula for the problem solution from resolvents of two integral equations. [ABSTRACT FROM AUTHOR]