Multiple radial solutions for a class of elliptic systems with singular nonlinearities

Abstract

We study radial solutions u=(ui, u%) in an exterior domain ofRN (N ≥4 3) of the elliptic system -Δu + V(u) = 0, where F is a positive and singular potential. We look for solutions which satisfy Dirichlet boundary conditions and vanish at infinity. We prove existence of infinitely many radial solutions, which can be topologically classified by their winding numbers around the singularity ofV. Furthermore, we study some qualitative properties of such solutions.