On the existence of positive solution for a class of singular systems involving quasilinear operators

Abstract In this paper we consider the existence of positive solution for the following class of singular systems - Δ p u = 1 v γ 1 + v α 1 , - Δ q v = 1 u γ 2 + u α 2 in Ω , u , v > 0 in Ω , u = v = 0 on ∂ Ω , where Ω ⊂ R N , N ⩾ 2 , is a smooth bounded domain, Δ p and Δ q are, respectively, the p -Laplacian and q -Laplacian, with p , q  > 1, and α 1 , α 2 , γ 1 and γ 2 are positive constants. The main tools used are a result due to Rabinowitz and a Hardy–Sobolev inequality.

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