LAUSR

Abstract We prove the existence of nonzero positive solutions of the p -Laplacian system { − Δ p u i = f i ( x , u )  in  Ω , i ∈ { 1 , . . , n } , u i = 0  on  ∂ Ω , where u = ( u 1 , . . , u n ) , Δ p u i = div ( | ∇ u i | p − 2 ∇ u i ) , p > 1 , Ω is a bounded domain in R n with smooth boundary ∂Ω, f i : Ω × R + n → R + are allowed to be singular at x ∈ ∂ Ω and satisfy some sublinear conditions. Our results improved previously known results in the literature.