Abstract

We study how a boundary value problem with a nonlocal integral condition of the first kind for a mixed type equation with a singular coefficient in a rectangular domain depends on a numerical parameter occurring in the equation. A uniqueness criterion is established, and theorems on the existence and stability of a solution of the problem are proved. The solution is constructed in closed form, and the convergence of the series in the class of regular solutions is justified.

中文翻译：

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具有奇异系数的混合型方程的积分条件的非局部边值问题

摘要

我们研究在矩形域中具有奇异系数的混合型方程的第一类具有非局部积分条件的边值问题如何取决于方程中出现的数值参数。建立了唯一性判据，证明了该问题解的存在性和稳定性。该解决方案以封闭形式构造，并且证明了该系列在常规解决方案类别中的收敛性。