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Fučík spectra for vector equations

By C. Fabry


Ω being open and bounded in R M. The aim of this paper is to study the Fučík spectrum for vector problems of the form Lu = αAu + −βAu − , where A is an N ×N matrix, α, β are real numbers, u + a vector defined componentwise by (u +)i = max{ui, 0}, u − being defined similarly. With λ ∗ an eigenvalue for the problem Lu = λAu, we describe (locally) curves in the Fučík spectrum passing through the point (λ ∗ , λ ∗), distinguishing different cases illustrated by examples, for which Fučík curves have been computed numerically. Key words:Nonlinear eigenvalue problems, asymmetric nonlinearities. AMS Classification:34B15, 35P30

Year: 2014
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