Infinitely many solutions for Δα-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 -Delta(alpha)u+ V(x)u = f(x,u)+ g(x)vertical bar u|vertical bar(q-2) u and -Delta(alpha)u+ V (x) u = f(x, u)+lambda u in Omega with u = 0 on partial derivative Omega , where Omega is a bounded domain in R-n, Delta(alpha) is the strongly degenerate operator, the functions alpha = (alpha(1),..., alpha(n)) : R-n -> R-n satisfies some certain conditions,. is a parameter, q is an element of (1, 2), and f : Omega x R -> R is a Caratheodory function and g is a function that we will specify later.