The solution of some persistent p : ?q resonant center problems

摘要

The notion of p : ?q resonant center was introduced recently and studied by several authors. In this paper we generalize the notion of a persistent center to a persistent p : ?q resonant center and find conditions for existence of a persistent p : ?q resonant center for several p : ?q resonant systems with quadratic nonlinearities. To prove the sufficiency of the obtained conditions we use either the Darboux theory of integrability or look for a formal first integral of the required form or we use the method based on the blow-up transformation.