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Locally minimising solutions of − Δu = u(1 − |u|2) in R2
Published online by Cambridge University Press: 14 November 2011
Abstract
We prove that locally minimising solutions of − Δu = u(1 − |u|2) in R2, i.e. solutions that minimise the action in any bounded domain of R2, are such that ∫R2(1 − |u|2)2(x) dx < + ∞. We prove a similar property for locally minimising solutions in a half-plane.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 349 - 358
- Copyright
- Copyright © Royal Society of Edinburgh 1998
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