An elliptic singular system with nonlocal boundary conditions

Abstract

We study the existence of solutions for the nonlinear second order elliptic system ∆u + g(u) = f(x), where g ∈ C(R N \ S, R N ) with S ⊂ R N bounded. Using topological degree methods, we prove an existence result under a geometric condition on g. 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.