Solvability of inhomogeneous boundary-value problems for fourth-order differential equations |
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Authors: | K. O. Buryachenko |
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Affiliation: | 1.Donetsk National University,Donetsk,Ukraine |
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Abstract: | We consider a Cauchy-type boundary-value problem, a problem with three boundary conditions, and the Dirichlet problem for a general typeless fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a bounded domain Ω ⊂ R 2 with smooth boundary. By the method of the Green formula, the theory of extensions of differential operators, and the theory of L-traces (i.e., traces associated with the differential operation L), we establish necessary and sufficient (for elliptic operators) conditions of the solvability of each of these problems in the space H m (Ω), m ≥ 4. |
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