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A blowing-up branch of solutions for a mean field equation

✍ Scribed by Marcello Lucia

Publisher: Springer
Year: 2006
Tongue: English
Weight: 388 KB
Volume: 26
Category: Article
ISSN: 0944-2669
DOI: 10.1007/s00526-006-0007-3

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✦ Synopsis

We consider the equationIf Ω is of class , we show that this problem has a non-trivial solution u λ for each λ ∊ (8π, λ). The value λ depends on the domain and is bounded from below by 2 j 0 2 π, where j 0 is the first zero of the Bessel function of the first kind of order zero (λ*≥ 2 j 0 2 π > 8 π). Moreover, the family of solution u λ blows-up as λ → 8 π.

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