Multiplicity theorems for a class of Dirichlet quasilinear elliptic systems involving the (p1,…,pn)(p1,…,pn)-Laplacian

In this paper, we prove the existence of at least three weak solutions for the quasilinear elliptic systems {Δp1u1+λFu1(x,u1,u2,…,un)=0inΩ,Δp2u2+λFu2(x,u1,u2,…,un)=0inΩ,…Δpnun+λFun(x,u1,u2,…,un)=0inΩ,ui=0for 1≤i≤non∂Ω. Our main tool is a recent three critical points theorem of Averna and Bonanno [D. Averna, G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal. 22 (2003) 93–104].