The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN.
The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis and F. de Thélin’s work [9] for the first property and A. Anane’s one for the isolation.
@article{urn:eudml:doc:41462,
title = {Extension of D\'\i az-Sa\'a's inequality in RN and application to a system of p-Laplacian.},
journal = {Publicacions Matem\`atiques},
volume = {46},
year = {2002},
pages = {473-488},
mrnumber = {MR1934366},
zbl = {1163.35392},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41462}
}
Chaïb, Karim. Extension of Díaz-Saá's inequality in RN and application to a system of p-Laplacian.. Publicacions Matemàtiques, Tome 46 (2002) pp. 473-488. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41462/