【摘要】 研究了特殊Ⅲ类二次微分系统x=-Y+lx2+mxy,y=x(1+ax+by)的极限环的最大个数问题.纠正了索明霞和岳锡亭的文章(微分方程年刊,2003,19(3):397-401)中的一些错误.通过将所研究的系统化为Lienard型系统并利用其相关性质给出了几个定理,在某些条件下证明了系统最多存在2个极限环,改进了上述一文中的结果.更多还原

【Abstract】 The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue’s paper mentioned above.更多还原