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