Abstract
In this paper, we obtain a necessary and sufficient condition for the nontrivial solvability of homogeneous Dirichlet problems in the disk for linear equations of arbitrary even order 2m with constant complex coefficients and homogeneous nondegenerate symbol in general position. The cases m=1, 2, 3 are studied separately. For the case m=2, we consider examples of real elliptic systems reducible to single equations with constant complex coefficients for which the homogeneous Dirichlet problem in the disk has a countable set of linearly independent polynomial solutions.
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Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 498–508.
Original Russian Text Copyright © 2005 by V. P. Burskii, E. A. Buryachenko.
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Burskii, V.P., Buryachenko, E.A. Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk. Math Notes 77, 461–470 (2005). https://doi.org/10.1007/s11006-005-0044-9
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DOI: https://doi.org/10.1007/s11006-005-0044-9