Nonuniqueness conditions for the solutions of the Dirichlet problem in a unit disk in terms of the coefficients of differential equation

被引：0

作者：

Il'kiv V.S. ^{[1
,2
]}

机构：

[1] L'vivs'ka Politekhnika National University, Lviv

[2] Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv

来源：

Journal of Mathematical Sciences | 2013年 / 194卷 / 2期

关键词：

Unit Disk; Dirichlet Problem; Cosn; Unique Solvability; Characteristic Slope;

D O I：

10.1007/s10958-013-1519-y

中图分类号：

学科分类号：

摘要：

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. © 2013 Springer Science+Business Media New York.

引用

页码：182 / 197

页数：15

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