关键词: Stability, Cauchy problem, asymptotic stability

Abstract: This article is contributed to the Cauchy problem
$$ \left\{\begin{array}{ll} \D
\frac{\partial u}{\partial t}=
\Delta u+K( |x|)u^p \ \ \mbox{in} \ R^n \times(0,T),\\
u(x,0)=\varphi(x) \ \ \mbox{in} \ R^n ;
\end{array}
\right. $$
with initial function $\varphi \not \equiv 0$. The stability of positive radial steady state, which are positive solutions of △u+K( | x|)u^p=0, is obtained when p is critical for general K(|x|).

Key words: Stability, Cauchy problem, asymptotic stability