A sufficient condition in order that the real Jacobian conjecture in \(\mathbb{R}^2\) holds (Q907801)

The author gives a partial result concerning the real Jacobian conjecture in \(\mathbb{R}^{2}:\) if \(F=(f,g):\mathbb{R}^{2}\mathbb{\rightarrow R}^{2}\) is a polynomial map such that \(\det DF\) is nowhere zero, \(F(0,0)=(0,0),\) and the higher homogeneous terms of the polynomials \(ff_{x}+gg_{x}\) and \( ff_{y}+gg_{y}\) do not have real linear factors in common, then \(F\) is injective.