研究一类m=6,n=8和一类m=8,n=6的Liénard系统在原点邻域内的极限环数目问题,证明了这两个系统在原点充分小邻域内分别能产生9个和8个极限环,首次给出了H^(6,8)和H^(8,6)的一个下界估计,即H^(6,8)≥9,H^(8,6)≥8。
The number of limit cycles for classes of Li6nard systems ( m = 6, n = 8 ) and ( m = 8, n = 6) in the neighborhood of the origin is studied. It is proved that the two systems can generate 9 and 8 limit cycles in a sufficiently small neighborhood of the origin, respectively. It is the first time that lower bound estimations of H(6,8) andH(8,6) are obtained, namelyH(6,8) ≥ 9,H(8,6) ≥8.