Positive radial solutions to classes of nonlinear elliptic systems on the exterior of a ball

We study positive radial solutions to n x n nonlinear elliptic systems of the form: {-Delta u(i) = lambda K-i (vertical bar x vertical bar)f(i )(u(i)+1) in x is an element of Omega(E), u(i) = 0 on vertical bar x vertical bar = r(0), u(i) -> 0 as vertical bar x vertical bar -> infinity where i is an element of {1,2, ..., n}, u(1) u(n+1), Delta u := div(del u), lambda > 0, N > 2, r(0) > 0, Omega(E) := {x is an element of R-N vertical bar x vertical bar > r(0)}, K-i is an element of C ((r(0), infinity), (0, infinity) and f(i) is an element of C([0, infinity), R). We establish existence, multiplicity and uniqueness results for various nonlinearities f(i). (C) 2020 Elsevier Inc. All rights reserved.