Local \(C^{\infty}\)-solvability of nonlinear functional equations (Q1074040)

The author studies the \(C^{\infty}\) local solvability of nonlinear functional equations of the form \((A\phi)(x)=0\) where \((A\phi)(x)=\phi (\Lambda x)-F(x,\phi (x));\) \(\Lambda\) : \({\mathbb{R}}^ n\to {\mathbb{R}}^ n\) is a linear operator and \(F: {\mathbb{R}}^ n\times {\mathbb{R}}^ m\to {\mathbb{R}}^ m\) is a \(C^{\infty}\) map.