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Generalized CR Equation with a Singularity
Abstract:This article deals with the solvability of the CR equation rw /></span> = (<i>A<sub>0</sub></i>(<i>θ</i>) ? <i>O</i>(<i>r</i><sup>α</sup>))<i>w</i> ? (<i>B</i><sub>0</sub>(<i>θ</i>) ? <i>O</i>(<i>r</i><sup>α</sup>))<span class= /></span>, where <i>z</i> = <i>r e<sup>iθ</sup></i> and where <i>A</i><sub>0</sub>, <i>B</i><sub>0</sub> are continuous and 2π-periodic. The solutions of this equation are shown to be similar to those of the model equation <i>rw</i><span class= /></span> = <i>A</i><sub>0</sub>(<i>θ</i>)<i>w</i> ? B<sub>0</sub>(<i>θ</i>)<span class= /></span>. The solutions of the model equation are completely characterized by using dynamical systems and Fourier techniques.</td> </tr> <tr> <td align=
Keywords:CR equation  Periodic systems  Fixed point  Similarity principle
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