On the Existence of Positive Solutions for Semilinear Elliptic Equations in the Annulus

We study the existence of positive radial solutions of Δu+g(x) ƒ(u) = 0 in annuli with Dirichlet (Dirichlet/Neumann) boundary conditions. We prove that the problems have positive radial solutions on any annulus if ƒ is sublinear at 0 and ∞.