Positive radial solutions to classes of singular problems on the exterior domain of a ball

We study positive radial solutions to singular boundary value problems of the form: {-Delta u = lambda K(vertical bar x vertical bar) f(u)/u(alpha), in Omega, partial derivative u/partial derivative eta + (c) over tilde (u)u = 0, vertical bar x vertical bar = r(0), u(x) -> 0, vertical bar x vertical bar -> infinity, where Delta u := div(del u) is the Laplacian operator of u, Omega = {x is an element of R-N vertical bar x vertical bar > r(0) > 0, N > 2}, lambda > 0, K is an element of C([r(0), infinity), (0, infinity)) is such that K(s) <= 1/s(N+beta) for s >> 1 for some (beta) over cap > 1, alpha < min{1, <(beta)over cap>/N-2} and partial derivative u/partial derivative eta is the outward normal derivative of u on vertical bar x vertical bar = r(0). Here, f is an element of C-1 ([0, infinity), R) is such that f(s)/s(1+alpha) -> 0 as s -> infinity, and (c) over tilde is an element of C([0, infinity), (0, infinity)). We analyse the cases when (a) f(0) > 0 and (b) f (0) < 0. We discuss existence, non-existence, multiplicity and uniqueness results. We prove our existence results by the method of sub and supersolutions. (C) 2015 Elsevier Inc. All rights reserved.