This paper deals with the existence of weak solutions of Neumann problem for a nonuniformly semilinear elliptic equation :
where
, is an unbounded domain with smooth and bounded boundary
,
,
,
,
as
, , , ,
are Carathéodory,
,
,
.
Our arguments is based on the minimum principle and rely essentially on a generalization of the Landesman-Lazer type condition.