Existence of large solutions for quasilinear elliptic problems with a gradient term

In this paper, we prove the existence of the positive large solutions for the equationdiv(|∇u|m-2∇u)+λ(|x|)|∇u|m-1=φ(x,u(x))div(|∇u|m-2∇u)+λ(|x|)|∇u|m-1=φ(x,u(x))in the whole space RN(N⩾3), where λ:[0,∞)→[0,∞)λ:[0,∞)→[0,∞) is a continuous function and m > 1, with φ:RN×[0,∞)→[0,∞)φ:RN×[0,∞)→[0,∞) is required to satisfy some hypotheses detailed blow. More precisely, we will give a sufficient and necessary condition for the existence of an entire large radial solution and a necessary condition for the existence of the entire large positive radial solution.