IMI/Publicaţii/BASM/Ediţii/BASM n.1 (11), 1993/

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

Authors: Shuba A. S.


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.

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