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Existence of solutions for a resonant Steklov Problem

Author(s): Aomar ANANE | Omar CHAKRONE | Belhadj KARIM | Abdellah ZEROUALI

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 27;
Issue: 1;
Start page: 85;
Date: 2009;
Original page

Keywords: Steklov problem | Weights | Landesman-Lazer conditions | Palais–Smale conditions.

In this paper, we prove the existence of weak solutions to the problem △_p u = 0 in Ω, |∇u|^{p−2} ∂_ν u = λ_1 m(x)|u|^{p−2}u + f(x, u) − h on ∂Ω, where Ω is a bounded domain in RN (N ≥ 2), m ∈ L^q(∂Ω) is a weight, λ_1 is the first positive eigenvalue for the eigenvalue Steklov problem △pu = 0 in Ω and |∇u|^{p−2} ∂_ν u=λ m(x)|u|^{p−2}u on ∂Ω. f and h are functions that satisfy some conditions.
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