Limit cycle problem for quadratic differential system x=-y+lx2+mxy,y=x(1+ax+by)

The maximal number of limit cycles for a particular type Ill 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.