摘要
Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y ＋ εhl1（x） ＋ ε2hl2（x）,y=-x- ε（fn1（x）y（2p＋1） ＋ gm1（x）） ＋ ∈2（fn2（x）y（2p＋1） ＋ gm2（x））,which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.
Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y ＋ εhl1（x） ＋ ε2hl2（x）,y=-x- ε（fn1（x）y（2p＋1） ＋ gm1（x）） ＋ ∈2（fn2（x）y（2p＋1） ＋ gm2（x））,which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.
