@article{Buryachenko_2011, title={Solvability of inhomogeneous boundary-value problems for fourth-order differential equations}, volume={63}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2781}, abstractNote={We consider a Cauchy-type boundary-value problem of, a problem with three boundary conditions, and the Dirichlet problem for a general fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a bounded domain $\Omega \subset R^2$ with smooth boundary. Using the method of the Green formula, the theory of expansion of differential operators, and the theory of $L$-traces (i.e., traces associated with a differential operation $L$), we obtain necessary and sufficient (for elliptic operators) conditions for the solvability of each of the problems under consideration in the space $H^m(\Omega),\;\; m \geq 4$.}, number={8}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Buryachenko, K. O.}, year={2011}, month={Aug.}, pages={1011-1020} }