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.