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

Published online by Cambridge University Press:  20 January 2009

Jann-Long Chern
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China (chern@math.ncu.edu.tw)
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Abstract

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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 μν ≥ 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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

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