Stability of steady states for the heat equation with nonlinear boundary conditions

We consider the following heat equation with nonlinear boundary conditions: ut=Δu in , ∂νu=uq on . This equation admits positive xn-axial symmetric steady states if and only if q⩾n/(n−2). In this paper, we study the stability of those positive xn-axial symmetric steady states for the case q>n/(n−2).