TY - JOUR

T1 - On the blow-up and positive entire solutions of semilinear elliptic equations

AU - Chern, Jann Long

N1 - Funding Information:
Work partly supported by the National Science Council of the

PY - 2000/10

Y1 - 2000/10

N2 - 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.

AB - 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.

KW - Blow-up

KW - Entire solutions

KW - Semilinear elliptic equations

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U2 - 10.1017/S0013091500021234

DO - 10.1017/S0013091500021234

M3 - Article

AN - SCOPUS:84858065634

SN - 0013-0915

VL - 43

SP - 625

EP - 631

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 3

ER -