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.

中文翻译：

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带伪抛物线微分算子的因式方程的一个问题

我们提出了一个四阶因式微分方程的新问题，它的算子是一阶和三阶微分算子的乘积，并证明了其独特的可解性。我们根据相应的三阶伪抛物型微分算子的Riemann函数构造解决方案，并根据两个积分方程的解析度确定要输入问题解决方案公式的函数之一。