In this paper we consider the following semilinear elliptic equation
where n ≥ 3, and β ≥ 0, γ ≥ 0, q > p ≥ 1, μ and ν are real constants. We note that if γ = 0, β > 0 and ν ≥ 2, then the equation above is called the Matukuma-type equation. If β = 0, γ > 0 and ν > 2, then the complete classification of all possible positive solutions had been conducted by Cheng and Ni. If β > 0, γ > 0 and μ ≥ ν ≥ 2, then some results about the maximal solution and positive solution structures can be found in Chern. The purpose of this paper is to discuss and investigate the blow-up and positive entire solutions of the equation above for the μ ≥ 2 ≥ ν case.