Abstract
This paper is a contribution to the analysis of the Cauchy problem (0.1){∂u∂t=Δu+∑i=1kci|x|liupiinRn×(0,T),u(x,0)=φ(x)inRn, with initial function φ≢0. The stability and asymptotic stability of the positive radial steady states, which are positive solutions of (0.2)Δu+∑i=1kci|x|liupi=0, have been discussed with φ in weighted Banach spaces.
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