The uniqueness of blow-up solution for radially symmetric semilinear elliptic equation

In this paper we establish a blow up rate of the large positive solutions of the singular boundary value problem - Δ u = λ u - b ( x ) u p , u | ∂ Ω =+ ∞ with a ball domain and radially function b ( x ) . All previous results in the literature assumed the decay rate of b ( x ) to be approximated by...

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Bibliographic Details
Published in:Nonlinear analysis 2006-05, Vol.64 (9), p.2129-2142
Main Authors: Ouyang, Tiancheng, Xie, Zhifu
Format: Article
Language:English
Subjects:
Blow up rate
Exact sciences and technology
Large positive solution
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Semilinear elliptic equation
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Summary:In this paper we establish a blow up rate of the large positive solutions of the singular boundary value problem - Δ u = λ u - b ( x ) u p , u | ∂ Ω =+ ∞ with a ball domain and radially function b ( x ) . All previous results in the literature assumed the decay rate of b ( x ) to be approximated by a distance function near the boundary ∂ Ω . Obtaining the accurate blow up rate of solutions for general b ( x ) requires more subtle mathematical analysis of the problem.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.08.010