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Minimum action solutions of non-linear elliptic equations in unbounded domains containing a plane

Published online by Cambridge University Press:  14 November 2011

Otared Kavian
Otared Kavian
Affiliation:
Analyse Numérique, Couloir 55-65, 5ème Etage, Université P. & M. Curie, 4, Place Jussieu, 75252 Paris, Cedex 05, France
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Synopsis

Let d ≧ 1 be an integer and ω ⊂ℝd a smooth bounded domain and consider the elliptic equation − Δu = g(u) on Ω = ℝ2 × ω. We prove that under (almost) necessary and sufficient conditions on the continuous function g: ℝm→ ℝm the above equation has a minimum-action solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 327 - 343
Copyright
Copyright © Royal Society of Edinburgh 1986

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