The Fučík Spectrum for the Negative p-Laplacian with Different Boundary Conditions

  • Dumitru Motreanu
  • Patrick Winkert
Part of the Springer Optimization and Its Applications book series (SOIA, volume 68)


This chapter represents a survey on the Fučík spectrum of the negative p-Laplacian with different boundary conditions (Dirichlet, Neumann, Steklov, and Robin). The close relationship between the Fučík spectrum and the ordinary spectrum is briefly discussed. It is also pointed out that for every boundary condition there exists a first nontrivial curve Open image in new window in the Fučík spectrum which has important properties such as Lipschitz continuity, being decreasing and a certain asymptotic behavior depending on the boundary condition. As a consequence, one obtains a variational characterization of the second eigenvalue λ 2 of the negative p-Laplacian with the corresponding boundary condition. The applicability of the abstract results is illustrated to elliptic boundary value problems with jumping nonlinearities.

Key words

Fučík spectrum p-Laplacian Boundary conditions Elliptic boundary value problems 

Mathematics Subject Classification

47A10 35J91 35K92 35J58 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité de PerpignanPerpignan CedexFrance
  2. 2.Institut für MathematikTechnische Universität BerlinBerlinGermany

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