Decay estimates for Wolff potentials in RN and gradient-dependent quasilinear elliptic equations

We prove decay estimates of positive weak solutions u∈D1,p(RN)∩C1(RN) and their gradients |∇u| of the p-Laplacian problem (10):00 and |∇u(x)|. Therefore, one of the main goal of this paper is to prove decay estimates for corresponding Wolff potentials in RN. The obtained decay estimates in conjunction with a sub-supersolution method, which is developed here for quasilinear elliptic equations, are then applied to prove the existence of positive solutions for classes of gradient-dependent quasilinear equations in the formu∈D1,p(RN):−Δpu=a(x)f(u,∇u).