一类Linard方程的极限环

LIMIT CYCLES OF A CLASS OF LI NARD EQUATIONS

证明了Ｌｉéｎａｒｄ方程当Ｆ′（Ｘ）具有两个零点时在原点外围最多有一个或两个极限环，依据Ｆ（Ｘ）有一个或三个零点．并由此证明了（Ⅱ）（ｍ＝０）当ａ２·十ａ４＜０，２Ｓ／ａ＞１时在原点外围最多有两个极限环．

in this paper, we discuss the Lienard equationIt is proved that if F (x) has two zero points, this equation has at most one or twolimit cycles surrounding the origin, according as F(x) has one or three zero points.And we prove the quadratic system (Ⅱ )(m=0) has at most two limit cycles surrounding the origin by using this result, for a2 + a4 < 0, 2s/a > 1.