In this paper, we prove the existence of weak solutions to the problem \Delta_p u = 0 in \Omega and |∇u|^{p−2}\frac{\partial u} {\partial \nu}= \lambda_1 m(x)|u|^{p−2}u + f(x, u) − h on \partial \Omega, where \Omega is a bounded domain in R^N (N ≥ 2), m ∈ L^q(\partial \Omega) is a weight, \lambda_1 is the first positive eigenvalue for the eigenvalue Steklov problem \Delta_pu = 0 in \Omega and |∇u|^{p−2} \frac{\partial u} {\partial \nu} =\lambda m(x)|u|^{p−2}u on \partial \Omega. f and h are functions that satisfy some conditions.
@article{9070,
title = {Existence of solutions for a resonant Steklov Problem - doi: 10.5269/bspm.v27i1.9070},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v27i1.9070},
language = {EN},
url = {http://dml.mathdoc.fr/item/9070}
}
Anane, Aomar; Chakrone, Omar; Karim, Belhadj; Zerouali, Abdellah. Existence of solutions for a resonant Steklov Problem - doi: 10.5269/bspm.v27i1.9070. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v27i1.9070. http://gdmltest.u-ga.fr/item/9070/