Existence of solutions for a resonant Steklov Problem

Boletim da Sociedade Paranaense de Matemática

关键词: Steklov problem;    Weights;    Landesman-Lazer conditions;    Palais–Smale conditions.;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown