Ground state solutions for a semilinear elliptic problem with a convection term

By a sub-supersolution method and a perturbed argument, we improve the earlier results concerning the existence of ground state solutions to a semilinear elliptic problem − Δ u + p ( x ) | ∇ u | q = f ( x , u ) , u > 0 , x ∈ R N , lim | x | → ∞ u ( x ) = 0 , where q ∈ ( 1 , 2 ] , p ( x ) ∈ C loc α ( R N ) for some α ∈ ( 0 , 1 ) , p ( x ) ⩾ 0 , ∀ x ∈ R N , and f : R N × ( 0 , ∞ ) → [ 0 , ∞ ) is a locally Hölder continuous function which may be singular at zero.