On the Stability of the Positive Radial Steady States for a Semilinear Cauchy Problem Involving Critical Exponents

This article is contributed to the Cauchy problem {∂u∂t=Δu+K(|x|)up in Rn×(0,T),u(x,0)=ϕ(x) in Rn; with initial function φ notequiv; 0. The stability of positive radial steady state, which are positive solutions of Δu+K(|x|)up=0Δu+K(|x|)up=0, is obtained when p is critical for general K(|x|).