摘要
当ｎ次微分系统ｘ′＝λｘ－ｙ＋Ｐｎ（ｘ，ｙ），ｙ′＝ｘ＋λｙ＋Ｑｎ（ｘ，ｙ）（ｎ≥２）化为Ａｂｅｌ方程ｄｚ／ｄθ＝Ａ（θ）ｚ３＋Ｂ（θ）ｚ２＋Ｃ（θ）ｚ后，利用λＡ（θ）的符号给出了判定Ａｂｅｌ方程极限环的几个准则：（１）当λＡ（θ）≥０且ｎ为偶数时方程无极限环；（２）若λＡ（θ）≤０时，则方程存在唯一极限环；（３）若λＡ（θ）≥０且ｎ为奇数，则方程最多只有两个极限环．
After transforming the n -degree differential systems x′=λx-y+P n(x,y), y′=x+λy+Q n(x,y)(n≥2) into Abel equations d z/ d θ=A(θ)z 3+B(θ)z 2+C(θ)z , we obtain several criterions to determine the limit cycles of the Abel equations according to the sign of λA(θ) :(1)when λA(θ) ≥0 and n be even, the equations have no limit cycles. (2)when λA(θ) ≤0,the equations have unique limit cycles. (3)if λA(θ) ≥0 and n be odd, the equations have at most two limit cycles.
出处
《福州大学学报（自然科学版）》
CAS
CSCD
1999年第1期9-11,共3页
Journal of Fuzhou University(Natural Science Edition)
基金
国家自然科学基金
