Existence results for a quasilinear elliptic problem with a gradient term via shooting method

In this article we consider the problem −∆pu − b (x) |∇u| p−1 = a (x) f (u) , u > 0 on R (N ≥ 3), lim|x|→∞ u(x) = 0. We prove that the considered problem has a bounded positive entire radial solution under some conditions on a, b and f . The method of proving theorems is essentially based on the shooting method. Our result, about the existence of radially symmetric solutions, seem to be the first result in the literature dealing with the singular effect of nonlinearity and combined with the non linear gradient term. 2000 Mathematics Subject Classification: 35J60.