Geodesic
Boundary eigencurve problems involving the \(p\)-Laplacian operator
Electronic journal of differential equations, Tome 2008 (2008)
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 
@article{EJDE_2008__2008__a75,
     author = {El Khalil,  Abdelouahed and Ouanan,  Mohammed},
     title = {Boundary eigencurve problems involving the {\(p\)-Laplacian} operator},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1177.35144},
     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/