Increasing sequences of positive evanescent solutions of nonlinear elliptic equations

We deal with the existence of a sequence of positive solutions of the following class of nonlinear elliptic problems div(a(||x||)∇u(x))+f(x,u(x))+g(||x||,x⋅∇u(x))=0div(a(||x||)∇u(x))+f(x,u(x))+g(||x||,x⋅∇u(x))=0, where x∈Rnx∈Rn and ||x||>R||x||>R, with the condition lim||x||→∞⁡u(x)=0. Our results are based on the iteration approach, in which we apply the subsolution and supersolution method developed by Noussair and Swanson. In this paper we do not assume either growth conditions on f   or the equality f(⋅,0)≡0f(⋅,0)≡0. We also describe how quickly solutions tend to zero.