Nonconstant positive radial solutions for Neumann problem involving the mean extrinsic curvature operator

Abstract

Let B be the unit ball in RN with N≥2. Let f∈C1([0,∞),R), f(0)=0, f(β)=β for some β∈(0,∞), f(s)<sfors∈(0,β),f(s)>sfors∈(β,∞) and f′(β)>λkr, where λkr 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(∇u1−|∇u|2)+u=f(u)inB,∂νu=0on∂B.