(untitled) (Journal of Partial Differential Equations, 2014)
In this work, we are interested to obtain some result of existence and nonexistence of positive weak solution for the following p-Laplacian system equationcase-Δ_piu_i=λ_if_i (u_1,…,u_m),in Ω, i=1,…,m, ui=0,on ∂Ω, ∀i=1,…,m,caseequation where Δ_piz=div(|∇z|^pi-2∇z), pi ≥ 1,λ_i,1 ≤ i ≤ m are a positive parameter, and Ω is a bounded domain in R^N with smooth boundary ∂Ω. The proof of the main results is based to the method of sub-supersolutions.