Li, Gongbao; Yan, Shusen; Yang, Jianfu

Author(s)

Li, Gongbao

Yan, Shusen

Yang, Jianfu

Publication Date

2005

Abstract

In this paper, we study the existence and limiting behavior of the mountain pass solutions of the elliptic problem —Δu = λf(u — q(x)) in Ω C ℝ²; u 0 on ∂Ω, where q is a positive harmonic function. We show that the 'vortex core' Aλ = {x ∈ Ω: uλ (x) > q(x)} of the solution uλ, shrinks to a global minimum point of q on the boundary ∂Ω as λ → + ∞. Furthermore, we show that for each strict local minimum x₀ point of q(x) on the boundary ∂Ω, there exists a solution uλ whose vortex core shrinks to this strict local minimum point x₀ as λ → +∞.

Citation

SIAM Journal on Mathematical Analysis, 36(5), p. 1444-1460

ISSN

1095-7154

0036-1410

Link

https://hdl.handle.net/1959.11/4284

Publisher

Society for Industrial and Applied Mathematics

Title

An Elliptic Problem Related to Planar Vortex Pairs

Type of document

Journal Article

Entity Type

Publication

Author(s)	Li, Gongbao Yan, Shusen Yang, Jianfu
Publication Date	2005
Abstract	In this paper, we study the existence and limiting behavior of the mountain pass solutions of the elliptic problem —Δu = λf(u — q(x)) in Ω C ℝ²; u 0 on ∂Ω, where q is a positive harmonic function. We show that the 'vortex core' Aλ = {x ∈ Ω: uλ (x) > q(x)} of the solution uλ, shrinks to a global minimum point of q on the boundary ∂Ω as λ → + ∞. Furthermore, we show that for each strict local minimum x₀ point of q(x) on the boundary ∂Ω, there exists a solution uλ whose vortex core shrinks to this strict local minimum point x₀ as λ → +∞.
Citation	SIAM Journal on Mathematical Analysis, 36(5), p. 1444-1460
ISSN	1095-7154 0036-1410
Link	https://hdl.handle.net/1959.11/4284
Publisher	Society for Industrial and Applied Mathematics
Title	An Elliptic Problem Related to Planar Vortex Pairs
Type of document	Journal Article
Entity Type	Publication

An Elliptic Problem Related to Planar Vortex Pairs

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