Geodesic
On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 818-823

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the class of polynomial differential systems of the form $\dot{x} =\,\lambda x\,-\,y\,+\,{{P}_{n}}\left( x,\,y \right)$ , $\dot{y} =\,x\,+\,\lambda y\,+\,{{Q}_{n}}\left( x,\,y \right)$ where ${{P}_{n}}$ and ${{Q}_{n}}$ are homogeneous polynomials of degree $n$ . For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.
DOI : 10.4153/CMB-2015-062-1
Mots-clés : 34C35, 34D30, polynomial differential system, limit cycles, differential equations on the cylinder 
Llibre, Jaume; Zhang, Xiang. On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 818-823. doi: 10.4153/CMB-2015-062-1
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-062-1/}
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