A homogeneous Cauchy type functional equation is an equation of the form
where and is an unknown function and are two increasing maps on which satisfy and certain additional conditions. Such functions are said to form a P-configuration in .
B. Paneah [Discrete Contin. Dyn. Syst. 10, No. 1–2, 497–505 (2004); erratum ibid. 11, No. 2–3, 744 (2004; Zbl 1057.39022)] showed that every continuously differential solution of the equation above is linear. In this paper the author by an analysis of P-configuration dynamical systems shows that the equation above and, in particular, the functional equation
have a continuous nonlinear solution.