This paper is contributed to the Cauchy problem{(frac(∂ u, ∂ t) = Δ u + K (| x |) up + μ f (| x |), in Rn × (0, T),; u (x, 0) = φ (x), in Rn,) with initial function φ ≢ 0. The monotonicity and stability of the positive radial steady states, which are positive solutions of Δ u + K (| x |) up + μ f (| x |) = 0, are discussed with K (| x |), f (| x |) and φ in weighted Banach spa...
