Positive radial solutions for a class of singular superlinear problems on the exterior of a ball with nonlinear boundary conditions

We discuss existence and nonexistence results of positive radial solutions to the problem {-Delta u - lambda K(vertical bar x vertical bar)f(u) in vertical bar x vertical bar < r(0), partial derivative u/partial derivative n + <(c)over bar>(u)i = 0 on vertical bar x vertical bar = r(0), u(x) -> 0 as vertical bar x vertical bar -> infinity, where Omega = {x is an element of R-N : vertical bar x vertical bar > r(0) > 0}, N > 2, f : (0, infinity) -> R is continuous, superlinear at infinity, and is allowed to be singular at 0 with no sign conditions near 0. (C) 2017 Elsevier Inc. All rights reserved.