Conditions of nontrivial solvability of the homogeneous Dirichlet problem for equations of any even order in the case of multiple characteristics without slope angles

• Date: 2010
• Main Authors: Buryachenko, E. A., Буряченко, Е. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2890
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $–i$,...