Solvability of the homogeneous Dirichlet problem in a disk for equations of order 2m in the case of multiple characteristics with inclination angles

Abstract

We obtain a criterion of nontrivial solvability of the homogeneous Dirichlet problem in a unit disk K for a general equation of even order 2m, m > 2 , with constant complex coefficients and a homogeneous degenerate symbol. The dependence between the multiplicity of roots of the characteristic equation and the existence of a nontrivial solution of the problem from the space $$ {C^{2m}}\left( {\overline K } \right) $$ in the case where the roots are not equal to ± i is established.