Existence and multiplicity of positive radial solutions for singular superlinear elliptic systems in the exterior of a ball

Abstract

We prove the existence and multiplicity of positive radial solutions to the nonlinear system{−Δui=λKi(|x|)fi(uj) in Ω,di∂ui∂n+c˜i(ui)ui=0 on |x|=r0,ui(x)→0 as |x|→∞, for a certain range of λ>0, where i,j∈{1,2},i≠j, Ω={x∈RN:|x|>r0>0}, N>2,di≥0, Ki:[r0,∞)→(0,∞), c˜:[0,∞)→[0,∞),fi:(0,∞)→R are continuous with possible singularity ±∞ at 0 and satisfy a combined superlinear condition at ∞.