RO  EN

Linear particular integrals and the problem of the center. (Russian)

Authors: Shuba A. S.

Abstract

It is proven that if the first focal value of the system
$$\dot x=y+\sum^n_{i+j=2}b_{ij}x^iy^j=P(x,y),\quad \dot y=-x -\sum^n_{i+j=2}c_{ij}x^iy^j=-Q(x,y),\quad n\ge 3,$$
vanishes and there exist $(n^2+n-4)/2$ invariant straight lines the origin is a centre.

Universitatea de Stat din Moldova
str. Mateevici 60, MD-2009 Chişinău, Moldova