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

Dumitru Motreanu () and Patrick Winkert ()
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Dumitru Motreanu: Université de Perpignan
Patrick Winkert: Technische Universität Berlin

Chapter Chapter 28 in Nonlinear Analysis, 2012, pp 471-485 from Springer

Abstract: Abstract 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 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.

Keywords: Fučík spectrum; p-Laplacian; Boundary conditions; Elliptic boundary value problems; 47A10; 35J91; 35K92; 35J58 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-3498-6_28

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DOI: 10.1007/978-1-4614-3498-6_28

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