|
ВИДЕОТЕКА |
Третья Российско-Китайская научная конференция по комплексному анализу, алгебре, алгебраической геометрии и математической физике
|
|||
|
A refinement of the Kovalevskaya theorem on analytic solvability of a Cauchy problem Alexander Znamenskiy Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk |
|||
Аннотация: Let \begin{equation}\label{eq0} P=z_n^m+\sum_{\alpha\in A} a_{\alpha}z^{\alpha} \end{equation} be a polynomial where $ A \subset \mathbb{Z}^{n-1}_{\geqslant 0}\times \{0,1,\ldots,m-1\} $ is a finite set of exponents. Consider a differential equation \begin{equation}\label{eq1} P( \mathcal{D})y=f \end{equation} with $f=\sum_{k\in \mathbb{Z}^n_{\geqslant 0} }{b_k x^k}$ given as a power series. Note that \begin{equation}\label{eeq4} \frac{\partial^{k}y}{ \partial x^k}(x',0)=y_k(x'), \;\; k=0,\ldots,m-1, \end{equation} where Theorem. \textit{If the right hand side A strict condition on Note that relaxation of the condition on Язык доклада: английский |