We consider the Dirichlet problem in a unit disk for the main-type partial differential equations with constant complex-valued coefficients whose symbols are forms of any even order. We establish the nonuniqueness conditions for the solution in terms of the coefficients of equation for the case where the angles of inclination of the complex characteristics exist. We construct some examples of equations for which the Dirichlet problem in a disk has nontrivial solutions and is not Noetherian.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 3, pp. 49–60, July–September, 2012.
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Il’kiv, V.S. Nonuniqueness conditions for the solutions of the Dirichlet problem in a unit disk in terms of the coefficients of differential equation. J Math Sci 194, 182–197 (2013). https://doi.org/10.1007/s10958-013-1519-y
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DOI: https://doi.org/10.1007/s10958-013-1519-y