Karl Wilhelm Bauer

Eine verallgemeinerte Darboux-Gleichung I@@@A generalized Darboux equation I

AbstractThe paper is concerned with the elliptic equation

Über differentialgleichungen der form\(F(z,\bar z)w_{z\bar z} - n(n + 1)w = 0\)

\begin{gathered} w_{z\bar z} + \left[ {\frac{{n (n + 1)}}{{(z - \bar z)^2 }} - \frac{{m (m + 1)}}{{(z + \bar z)^2 }} + \frac{{q (q + 1)}}{{(1 + z\bar z)^2 }} - \frac{{p (p + 1)}}{{(1 - z\bar z)^2 }}} \right]w = 0, \hfill \\ n, m, p, q \in \mathbb{N}_0 . \hfill \\ \end{gathered}

Ueber die Einwirkung von Brom auf Fluoren und Fluorenon

General representation theorems for, the solutions are derived by differential operators if three parameters are different from zero or two parameters are equal. Some applications are given to pseudo-analytic functions and generalized Tricomi equations.AbstractThe paper is concerned with the elliptic equation

Allgemeine Darstellungssätze bei einer Klasse partieller Differentialgleichungen gerader Ordnung

\begin{gathered} w_{z\bar z} + \left[ {\frac{{n(n + 1)}}{{(z - \bar z)^2 }} - \frac{{m(m + 1)}}{{(z + \bar z)^2 }} + \frac{{q(q + 1)}}{{(1 + z\bar z)^2 }} - \frac{{p(p + 1)}}{{(1 - z\bar z)^2 }}} \right]w = 0, \hfill \\ n,m,p,q \in \mathbb{N}_0 . \hfill \\ \end{gathered}

A generalized Darboux equation II.

General representation theorems for the solutions are derived by differential operators if three parameters are different from zero or two parameters are equal. Some applications are given to pseudo-analytic functions and generalized Tricomi equations.