LAUSR

Abstract Let B be the unit ball in R N with N ≥ 2 . Let f ∈ C 1 ( [ 0 , ∞ ) , R ) , f ( 0 ) = 0 , f ( β ) = β for some β ∈ ( 0 , ∞ ) , f ( s ) s for s ∈ ( 0 , β ) , f ( s ) > s for s ∈ ( β , ∞ ) and f ′ ( β ) > λ k r , where λ k r is the k-th radial eigenvalue of − Δ + I in the unit ball with Neumann boundary condition. We use the unilateral global bifurcation theorem to show the existence of nonconstant, positive radial solutions of the quasilinear Neumann problem − div ( ∇ u 1 − | ∇ u | 2 ) + u = f ( u ) in B , ∂ ν u = 0 on ∂ B .