Abstract

For a mixed-type equation of the second kind with a singular coefficient by the spectral expansions uniqueness criterion is installed for solving the first boundary-value problem. The solution was constructed as the sum of a Fourier–Bessel series. In justifying the uniform convergence appeared the problem of small denominators. In connection with this evaluation is set on a small separation from zero denominator with the corresponding asymptotic behavior that allowed to justify the convergence of the series in the class of regular solutions.

中文翻译：

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具有特征退化和奇异系数的混合型方程的狄利克雷问题

摘要

对于具有通过谱扩展的奇异系数的第二种混合类型方程，安装唯一性准则来解决第一个边值问题。该解被构造为傅里叶-贝塞尔级数的总和。在证明统一收敛时，出现了小分母的问题。与该评估相关的是，将零分母与相应的渐近行为相距很小，从而证明该序列在正则解类中的收敛是正确的。