Solvability of inhomogeneous boundary-value problems for fourth-order differential equations
AbstractWe 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 $H^m(\Omega),\;\; m \geq 4$.
How to Cite
Buryachenko, K. O. “Solvability of Inhomogeneous Boundary-Value Problems for Fourth-Order Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 8, Aug. 2011, pp. 1011-20, https://umj.imath.kiev.ua/index.php/umj/article/view/2781.