  In this article we study ergodic problems in the whole space R m for viscous
Hamilton-Jacobi Equations in the case of locally Lips-chitz continuous and
coercive right-hand sides. We prove in particular the existence of a critical
value $\lambda$ * for which (i) the ergodic problem has solutions for all
$\lambda$ $\le$ $\lambda$ * , (ii) bounded from below solutions exist and are
associated to $\lambda$ * , (iii) such solutions are unique (up to an additive
constant). We obtain these properties without additional assumptions in the
superquadratic case, while, in the subquadratic one, we assume the right-hand
side to behave like a power. These results are slight generalizations of
analogous results by N. Ichihara but they are proved in the present paper by
partial differential equations methods, contrarily to N. Ichihara who is using
a combination of pde technics with probabilistic arguments.
