2017
Том 69
№ 9

All Issues

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.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 5, pp 676-690.

Citation Example: Buryachenko E. A. Conditions of nontrivial solvability of the homogeneous Dirichlet problem for equations of any even order in the case of multiple characteristics without slope angles // Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 591–603.

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