This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff
type −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω. Under bounded condition on M and some novel and periodic condition on F, some new
results of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained by
means of Bonanno's multiple critical points theorems without the Palais-Smale condition
and Ricceri's three critical points theorem, respectively
