Infinitely many solutions for Δ α -Laplaceequations with sign-changing potential

In this paper, we use some critical point theorems to discuss the existence of weak solutions for the nonlinear elliptic equations - Δ αu+ V(x) u= f(x, u) + g(x) | u| q-2u and - Δ αu+ V(x) u= f(x, u) + λu in Ω with u= 0 on ∂Ω , where Ω is a bounded domain in Rn, Δ α is the strongly degenerate operator, the functions α=(α1,…,αn):Rn→Rn satisfies some certain conditions, λ is a parameter, q∈ (1 , 2) , and f: Ω × R→ R is a Carathéodory function and g is a function that we will specify later.