Solvability of inhomogeneous boundary-value problems for fourth-order differential equations - Buryachenko, K. O. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
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 $Ω \subset R^2$ 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 $H^m(Ω),\;\; m ≥ 4$.