Sign-changing solutions for Schrِdinger equations with indefinite supperlinear nonlinearities

In this paper, we obtain existence of ground state solutions and ground state sign-changing solutions for the following Schrödinger equation { − Δ u + V ( x ) u = K ( x ) | u | p − 2 u in  R N u → 0 as  | x | → + ∞ , where N ≥ 3 , 2 < p < 2 ∗ : = 2 N / ( N − 2 ) , V ( x ) and K ( x ) are sign-changing functions satisfying very mild assumptions. The proofs rely on a new perturbed method which we design in this paper.