Article contents
A generic property of the resonance set of an elliptic operator with respect to the domain*
Published online by Cambridge University Press: 14 November 2011
Extract
The set of points (α, β) ∈ℝ2 for which the problem − δu = αu+ − βu− in Ω, u = 0 on ∂Ω(u+ = max {u, o} and u− = min {−u, 0}) has nontrivial solutions is important for the study of certain nonlinear problems. It is shown that for ‘most’ bounded domains Ω in ℝn, such a set is locally the union of a finite number of curves.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1301 - 1310
- Copyright
- Copyright © Royal Society of Edinburgh 1997
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