Open AccessOn the Fredholm Alternative for the Fučík Spectrum
Author(s) -
Pavel Drábek,
Stephen B. Robinson
Publication year - 2010
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2010/125464
Subject(s) - mathematics , spectrum (functional analysis) , fredholm integral equation , laplace operator , fredholm theory , boundary (topology) , characterization (materials science) , dirichlet distribution , pure mathematics , mathematical analysis , boundary value problem , integral equation , physics , materials science , quantum mechanics , nanotechnology
We consider resonance problems for the one-dimensional p-Laplacian assumingDirichlet boundary conditions. In particular, we consider resonance problems associatedwith the first three curves of the Fučík Spectrum. Using variational argumentsbased on linking theorems, we prove sufficient conditions for the existence of at leastone solution. Our results are related to the classical Fredholm Alternative for linearoperators. We also provide a new variational characterization for points on the thirdFučík curve
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