摘要：In this article, we discuss the existence of weak solution for the nonlinear system −div ( h 1 (|∇u| p ) |∇u| p−2 ∇u ) = f(x,u,v) in Ω, −div ( h 2 (|∇v| p ) |∇v| p−2 ∇v ) = g(x,u,v) in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth open set in R n , p ≥ 2 and h 1 ,h 2 ∈ C(R,R). Using variational methods, under suitable assumptions on the nonlinearities, we show the existence of weak solution.
