  Context. The external regions of galaxy clusters may be under strong
influence of the dark energy, discovered by observations of the SN Ia at
redshift z < 1. Aims. The presence of the dark energy in the gravitational
equilibrium equation, with the Einstein $\Lambda$ term, contrasts the gravity,
making the equilibrium configuration more extended in radius. Methods. In this
paper we derive and solve the kinetic equation for an equilibrium configuration
in presence of the dark energy, by considering the Newtonian regime, being the
observed velocities of the galaxies inside a cluster largely smaller than the
light velocity. Results. The presence of the dark energy in the gravitational
equilibrium equation leads to wide regions in the $W_0-\rho_{\Lambda}$ diagram
where the equilibrium solutions are not permitted, due to the prevalence of the
effects of the dark energy on the gravity.
