On the characterization of generalized Dhombres equations having non constant local analytic or
formal solutions

Abstract. We discuss solvability conditions of the generalized Dhombres functional equation in the complex domain. Our focus lies on the so-called 'infinity' case, but also the \(z_0\)–case is investigated. That means that we consider solutions of a generalized Dhombres equation with initial value \(f(\infty)=w_0\), \(w_0 \neq 0\), or \(f(\infty)=\infty\), or \(f(z_0)=1\) for \(z_0 \neq 0, \infty\). For both situations we give a characterization of the generalized Dhombres equations which are solvable.