On the maximum number of limit cycles of certain polynomial Lienard equations.

摘要

We consider the Lienard equation of the form;We establish a sharp upper bound for the number of limit cycles (nontrivial isolated periodic orbits of system (2) depending on m and the degree of f provided ;This result is an important step in the study of planar polynomial vector fields in connection with the second part of Hilbert's Sixteenth Problem, which is still an open question.