An elliptic singular system with nonlocal boundary conditions

We study the existence of solutions for the nonlinear second order elliptic system Δu+g(u)=f(x)Δu+g(u)=f(x), where g∈C(RN∖S,RN)g∈C(RN∖S,RN) with S⊂RNS⊂RN bounded. Using topological degree methods, we prove an existence result under a geometric condition on gg. Moreover, we analyze the particular case of an isolated repulsive singularity: under a Nirenberg type condition, we prove the existence of a sequence of solutions of appropriate approximated problems that converges to a generalized solution.