Abstract

Let B be the unit ball in RN, N = 5 and n be the exterior unit normal vector on the boundary. We consider radial solutions to?2 u = ? eu in B, u = 0 and frac(? u, ? n) = 0 on ? B, where ? = 0. We show that there exists a unique ?S > 0 such that if ? = ?S there is a radial singular solution. If 5 = N = 12 then for ? = ?S there exist infinitely many regular radial solutions and as ? ? ?S the number of such solutions goes to infinity. If N = 13 we prove uniqueness of smooth radial solutions. We derive similar results for the same equation with Navier boundary conditions. © 2009 Elsevier Inc. All rights reserved.