On the Fucik spectrum and a resonance problem for the <i>p</i>-Laplacian with a nonlinear boundary condition
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2004
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Abstract
In this paper we prove that there exists a first curve of the Fucik spectrum of the problem Deltapu = \u\(p-2)u in Omega with a nonlinear boundary condition given by \delu\(p-2)partial derivativeu/partial derivativev=alpha(u(+))(p-1)-beta(u(-))(p-1) on the boundary of the domain. We also prove that there exists a sequence of curves of the Fucik spectrum which exist locally in the neighborhood of suitable eigenvalues of the p-Laplacian with a nonlinear boundary condition. Finally, we study a resonance problem with respect to the Fucik spectrum. (C) 2004 Published by Elsevier Ltd.
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Keywords
p-Laplacian, nonlinear boundary conditions, resonance