On the uniqueness of singular solutions for a Hardy-Sobolev equation

Jann Lgng Chern; Ygng Li Tang; Chuan Jen Chyan; Yi Jung Chen

On the uniqueness of singular solutions for a Hardy-Sobolev equation

Jann Lgng Chern, Ygng Li Tang, Chuan Jen Chyan, Yi Jung Chen

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider the positive singular solutions for the following Hardy-Sobolev equation Δu+u^p+u ^2*(s)-1/|x|^s=0 in B₁\{0}, where p > 1, 0 < s < 2, 2*(s) = 2(n-s)/n-2, n ≥ 3 and B₁ is the unit ball in Rⁿ centered at the origin. We prove that if p > ""+1 then such solution is unique.

Original language	English
Pages (from-to)	123-128
Number of pages	6
Journal	Discrete and Continuous Dynamical Systems - Series S
Issue number	SUPPL.
Publication status	Published - 2013 Nov
Externally published	Yes

Keywords

Hardy-Sobolev equation
Singular solution
Uniqueness of solutions

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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abstract = "In this paper, we consider the positive singular solutions for the following Hardy-Sobolev equation Δu+up+u 2*(s)-1/|x|s=0 in B1\{0}, where p > 1, 0 < s < 2, 2*(s) = 2(n-s)/n-2, n ≥ 3 and B1 is the unit ball in Rn centered at the origin. We prove that if p > {"}{"}+1 then such solution is unique.",

keywords = "Hardy-Sobolev equation, Singular solution, Uniqueness of solutions",

author = "Chern, {Jann Lgng} and Tang, {Ygng Li} and Chyan, {Chuan Jen} and Chen, {Yi Jung}",

year = "2013",

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AU - Tang, Ygng Li

AU - Chyan, Chuan Jen

AU - Chen, Yi Jung

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Y1 - 2013/11

N2 - In this paper, we consider the positive singular solutions for the following Hardy-Sobolev equation Δu+up+u 2*(s)-1/|x|s=0 in B1\{0}, where p > 1, 0 < s < 2, 2*(s) = 2(n-s)/n-2, n ≥ 3 and B1 is the unit ball in Rn centered at the origin. We prove that if p > ""+1 then such solution is unique.

AB - In this paper, we consider the positive singular solutions for the following Hardy-Sobolev equation Δu+up+u 2*(s)-1/|x|s=0 in B1\{0}, where p > 1, 0 < s < 2, 2*(s) = 2(n-s)/n-2, n ≥ 3 and B1 is the unit ball in Rn centered at the origin. We prove that if p > ""+1 then such solution is unique.

KW - Hardy-Sobolev equation

KW - Singular solution

KW - Uniqueness of solutions

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IS - SUPPL.

ER -

On the uniqueness of singular solutions for a Hardy-Sobolev equation

Abstract

Keywords

ASJC Scopus subject areas

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