Conditions of nontrivial solvability of the homogeneous Dirichlet problem for equations of any even order in the case of multiple characteristics without slope angles - Buryachenko, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We consider the homogeneous Dirichlet problem in the unit disk K ⊂ R^2 for a general typeless differential equation of any even order 2m, m ≥ 2, with constant complex coefficients whose characteristic equation has multiple roots ± i. For each value of multiplicity of the roots i and –i, we either formulate criteria of the nontrivial solvability of the problem or prove that the analyzed problem possesses solely the trivial solution. A similar result generalizes the well-known Bitsadze examples to the case of typeless equations of any even order.