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Boundary eigencurve problems involving the p-Laplacian operator

Author(s): Abdelouahed El Khalil | Mohammed Ouanan

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2008;
Issue: 78;
Start page: 1;
Date: 2008;
Original page

Keywords: p-Laplacian operator | nonlinear boundary conditions | principal eigencurve | Sobolev trace embedding

In this paper, we show that for each $lambda in mathbb{R}$, there is an increasing sequence of eigenvalues for the nonlinear boundary-value problem $$displaylines{ Delta_pu=|u|^{p-2}u quad hbox{in } Omegacr | abla u|^{p-2}frac{partial u}{partial u}=lambda ho(x)|u|^{p-2}u+mu|u|^{p-2}u quad hbox{on } partial Omega,; }$$ also we show that the first eigenvalue is simple and isolated. Some results about their variation, density, and continuous dependence on the parameter $lambda$ are obtained.
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