Abstract: In this paper the authors construct a quartic Abelian equation with coefficients beingtrig onometric polynomials of degree ≤3, in which there exist six periodic solutions. In other words, the authors give an example on Pugh's problem, in which K(n)=6 for n=4. The authors propose to comparethe example with Nirenberg's example, of which Smale spoke in[1].

Key words: Pugh''s problem, Poincare equation, Perturbation, Limit cycle