Virial theorem in scalar tensor fourth order gravity

In this paper, we study, in the Newtonian limit, the virial theorem in the context of a scalar tensor fourth order gravity. In particular, we show, that for a isolated galaxy in viral equilibrium, a specific class of scalar tensor fourth order gravity, i.e. f(R, $\varphi$) + $\omega$($\varphi$) ${\varphi }_{;\alpha }$${\varphi }^{;\alpha }$ in not suitable to explain the large fraction of dark matter necessary to have the flatness of the galaxies rotation curves experimentally observed.