Existence of positive solutions for a quasilinear elliptic system of p -Kirchhoff type

摘要

In this paper, we consider the existence of positive solutions to the following p - Kirchhoff-type system . . . . . . . .M Ω | . u| p dx Δ p u = g(x)|u| q.2 u + α α + β |u| α .2 u|v| β , x ∈ Ω , .M Ω | . u| p dx Δ p v = h(x)|v| q.2 v + β α + β |u| α |v| β .2 v, x ∈ Ω , u = v = 0, x ∈ . Ω , where Ω is a bounded domain in R N , M(s)=a + bs k , Δ p u = div(| . u| p.2 . u) is the p - Laplacian operator, α > 1, β > 1, 1 < p < q < α + β < p . = Np N.p .