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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 8, pp. 1011–1020, August, 2011.
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Buryachenko, K.O. Solvability of inhomogeneous boundary-value problems for fourth-order differential equations. Ukr Math J 63, 1165–1175 (2012). https://doi.org/10.1007/s11253-012-0570-z
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DOI: https://doi.org/10.1007/s11253-012-0570-z