Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 78, pp. 1-13.

Title: Boundary eigencurve problems involving
       the p-Laplacian operator
  
Authors: Abdelouahed El Khalil (Al-Imam Muhammad Ibn Saud Islamic Univ. Saudi Arabia)
         Mohammed Ouanan       (Univ. Moulay Ismail, Morocco)

Abstract: 
 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
 $$\displaylines{
 \Delta_pu=|u|^{p-2}u \quad \hbox{in }   \Omega\cr
 |\nabla u|^{p-2}\frac{\partial u}{\partial \nu}=\lambda
 \rho(x)|u|^{p-2}u+\mu|u|^{p-2}u \quad \hbox{on } \partial \Omega\,;
 }$$
 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.

Editor's note:
After publication, we learned that this article is an unauthorized
copy of 
"On the principal eigencurve of the p-Laplacian related to the 
Sobolev trace embedding", Applicationes Mathematicae, 32, 1 (2005), 1-16.
The authors alone are responsible for this action which 
may be in violation of the Copyright Laws.
 
Submitted September 16, 2007. Published May 27, 2008.
Math Subject Classifications: 35P30, 35J20, 35J60.
Key Words: p-Laplacian operator; nonlinear boundary conditions;
           principal eigencurve; Sobolev trace embedding.