On the blow-up and positive entire solutions of semilinear elliptic equations

In this paper we consider the following semilinear elliptic equation Δ+ where n ≥ 3, A = Σ (d ²/dx ²), and β 0, ≤ 0 , q ≤ p 1, μ and v are real constants. We note that if γ = 0, β > 0 and y. 2, then the equation above is called the Matukuma-type equation. If β = 0, γ > 0 and μ ≥ v > 2, then the complete classification of all possible positive solutions had been conducted by Cheng and Ni. If β > 0, γ > 0 and μ > 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 ≤ case.