Asymptotic estimates for PDE with p-Laplacian and damping

We study the positive solutions of equation div(||∇u||∇u) + ~b(x), ||∇u||∇u + c(x)|u|u = 0, via the Riccati technique and prove an integral sufficient condition on the potential function c(x) and the damping ~b(x) which ensures that no positive solution of the equation satisfies a lower (if p > q) or upper (if q > p) bound eventually.