Solutions of quasilinear elliptic equations in RN decaying at infinity to a non-negative number

We deal with existence of entire solutions for the quasilinear elliptic problem {-Delta(p)u = lambda a(x)f(u) in R-N, u>l in R-N, u(x) (vertical bar x vertical bar ->infinity) -> l, where 1 < p <N, N >= 3, l >= 0, Delta(p) is the p-Laplacian operator, lambda > 0 is a parameter, a:R-N -> (0, infinity) and f:(0, infinity) -> (0, infinity) are suitable functions. When l = 0, f is allowed to behave at 0 like f(s) (s -> 0) ->infinity. The potential a(x) will be required to decay to zero at infinity fast enough. Our technique explores variational principles, symmetry arguments as well as lower and upper solutions.