In this article, we study the following degenerated Schrödinger equations: −∆γu + λV(x)u = f(x, u) in RN, u ∈ Eλ , where λ > 0 is a parameter, ∆γ is a degenerate elliptic operator, the potential V(x) has a potential well with bottom and the nonlinearity f(x, u) is either super-linear or sub-linear at infinity in u. The existence of ground state solution be obtained by using the variational methods
