On a class of nonlocal elliptic systems of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:…

In this paper, we establish the existence of at least three solutions for the following nonlocal elliptic system of (p,q)-Kirchhoff type -M1∫Ω|∇u|pdxp-1Δpu=λFu(x,u,v)+μGu(x,u,v) in Ω,-M2∫Ω|∇v|qdxq-1Δqv=λFv(x,u,v)+μGv(x,u,v) in Ω,u=v=0 on ∂Ω. Our technical approach is based on the three critical points theorem of Ricceri