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Generic properties of the Fucik spectrum of elliptic operators

Published online by Cambridge University Press:  11 July 2007

B. P. Rynne
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK

Abstract

Given a bounded smooth domain Ω ⊂ Rn, n ≥ 2, and a second-order elliptic self-adjoint operator A on Ω, the set of points (α, β) ∈ R2 for which the problem Au = αu+ − βu- in Ω, u = 0 on ∂Ω (where u± = max{±u, 0}), has a non-trivial solution is called the Fucik spectrum of A. In this note we extend some recent results of Pistoia on the structure of this set for generic operators A (the genericity is with respect to the domain Ω or the coefficients of A).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

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