In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study the solvability of the problem \mathcal{A}u = -div (A(x,\nabla u)) = f(x,u) + h, in \Omega, u=0 on \partial \Omega, as well as the spectrum of G_0'(u)= \lambda m |u|^{p-2}u in \Omega, u=0 on \partial \Omega.
@article{10815,
title = {Eigenvalues of an Operator Homogeneous at the Infinity - 10.5269/bspm.v28i1.10815},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {28},
year = {2010},
doi = {10.5269/bspm.v28i1.10815},
language = {EN},
url = {http://dml.mathdoc.fr/item/10815}
}
Chakrone, Omar; Anane, Aomar; Filali, Mohammed; Karim, Belhadj. Eigenvalues of an Operator Homogeneous at the Infinity - 10.5269/bspm.v28i1.10815. Boletim da Sociedade Paranaense de Matemática, Tome 28 (2010) . doi : 10.5269/bspm.v28i1.10815. http://gdmltest.u-ga.fr/item/10815/