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{−Δu=λK(|x|)f(u)in |x|>r0,∂u∂n+c˜(u)u=0on |x|=r0,u(x)→0 as |x|→∞, where Ω={x∈RN:|x|>r0>0},N>2,f:(0,∞)→R is continuous, superlinear at ∞, and is allowed to be singular at 0 with no sign conditions near 0.