Abstract: In this paper, the authors discuss the following spatially inhomogeneous Boltzmann equation
\frac{\partial f}{\partial t} + \xi\cdot \nabla_{x}f(t, x, \xi) = Q(f, f).
By means of a new iteration method, the existence of a positive eternal solution with initial data close to a travelling Maxwellian is proved in the case of hard potentials with angular cut-off. Hence, the authors give a negative answer to the conjecture of Villani [12, 13] in the case of unbounded space domain.

Key words: Boltzmann equation, Kaniel-Shinbrot iteration, Eternal solution