Weak center for a class of $\Lambda$–$\Omega$ differential systems

Abstract

In this paper, we give the necessary and sufficient conditions for a class of higher degree polynomial systems to have a weak center. As corollaries, we prove the correctness of the two conjectures about the weak center problem for the $\Lambda$–$\Omega$ differential systems.

Keywords

• weak center
• $\lambda$–$\omega$ system
• composition center
• center conditions