Limit cycle uniqueness for a class of planar dynamical systems (Q1031711)

The paper contains the proof of a theorem concerning the uniqueness of a limit cycle for the system \[ \dot{x}=\beta(x)(\varphi(y)-F(x,y)),\quad \dot{y}=-\alpha(y)g(x), \] where \(\alpha(y)\) and \(\beta(x)\) are assumed to be positive. The theorem is applied to such systems in the case \(F(x,y)=F(x)v(y),\) where \(v(y)\) vanishes at some point.