Geodesic
Boundary eigencurve problems involving the $p$-Laplacian operator
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we show that for each $$\displaylines{ \Delta_pu=|u|^{p-2}u \quad \hbox{in } \Omega\cr |\nabla u|^{p-2}\frac{\partial u}{\partial \nu}=\lambda \rho(x)|u|^{p-2}u+\mu|u|^{p-2}u \quad \hbox{on } \partial \Omega\; }$$ 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.
Classification : 35P30, 35J20, 35J60
Keywords: p-Laplacian operator, nonlinear boundary conditions, principal eigencurve, Sobolev trace embedding 
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     author = {El Khalil, Abdelouahed and Ouanan, Mohammed},
     title = {Boundary eigencurve problems involving the $p${-Laplacian} operator},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a75/}
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El Khalil, Abdelouahed; Ouanan, Mohammed. Boundary eigencurve problems involving the $p$-Laplacian operator. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a75/