Abstract
Let B be the unit ball in R N , N ⩾ 5 and n be the exterior unit normal vector on the boundary. We consider radial solutions to Δ 2 u = λ e u in B , u = 0 and ∂ u ∂ n = 0 on ∂ B , where λ ⩾ 0 . We show that there exists a unique λ S > 0 such that if λ = λ S there is a radial singular solution. If 5 ⩽ N ⩽ 12 then for λ = λ S there exist infinitely many regular radial solutions and as λ → λ 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.
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