Abstract

In an unbounded domain, for a class of equations of mixed type with a singular coefficient, the correctness of the problem is studied in which one of the internal characteristics is freed from the Gellerstedt condition and this missing local condition is replaced by an analogue of the Frankl condition on the degeneration line. The uniqueness of the solution to the stated problem is proved using the extremum principle, while the existence of a solution to the problem is proved by the method of integral equations.

中文翻译：

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一类混合型方程组退化线段Frankl条件和缺失Gellerstedt条件的无界域问题

摘要

在无界域中，对于一类具有奇异系数的混合型方程，研究了问题的正确性，其中一个内部特征不受盖勒施泰特条件的影响，并且用下式的类似物代替了该缺失的局部条件。退化线上的弗兰克尔条件。利用极值原理证明了该问题解的唯一性，而利用积分方程的方法证明了该问题解的存在性。