Generic properties of the Fucik spectrum of elliptic operators

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Abstract

Given a bounded smooth domain O ? Rn, n = 2, and a second-order elliptic self-adjoint operator A on O, the set of points (a, ß) ? R2 for which the problem Au = au+ - ßu- in O, u = 0 on ?O (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 O or the coefficients of A).

Original languageEnglish
Pages (from-to)217-224
Number of pages8
JournalProceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume130
Issue number1
Publication statusPublished - 2000

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