Geodesic
Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 498-508

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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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     author = {V. P. Burskii and E. A. Buryachenko},
     title = {Some aspects of the nontrivial solvability of homogeneous {Dirichlet} problems for linear equations of arbitrary even order in the disk},
     journal = {Matemati\v{c}eskie zametki},
     pages = {498--508},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a1/}
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V. P. Burskii; E. A. Buryachenko. Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 498-508. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a1/