Multiplicity of solutions for a class of (p_1,p_2,…,p_n) -Laplacian elliptic systems with a nonsmooth potential

In this paper, we prove that the following (p_1,p_2,…,p_n) -Laplacian elliptic system with a nonsmooth potential has at least three weak solutions: -Δ _p_1u_1+b_1(x) | u_1| ^p_1-2u_1∈λ∂ _u_1F(x,u_1,…,u_n) , ⋯ -Δ _p_nu_n+b_n(x) | u_n| ^p_n-2u _n∈λ∂ _u_nF(x,u_1,…,u_n) , u_i=0 1≤ i≤ n ∂. The proof is based on a three critical points theorem for nondifferentiable functionals. Some recent results in the literature are generalized and improved.