LAUSR

The aim of this paper is to investigate the existence of proper, weakly biharmonic maps within a family of rotationally symmetric maps $$u_a : B^n \rightarrow {\mathbb {S}}^n$$ u a : B n → S n , where $$B^n$$ B n and $${\mathbb {S}}^n$$ S n denote the Euclidean n -dimensional unit ball and sphere respectively. We prove that there exists a proper, weakly biharmonic map $$u_a$$ u a of this type if and only if $$n=5$$ n = 5 or $$n=6$$ n = 6 . We shall also prove that these critical points are unstable.