Least energy nodal solution for nonlinear Schrödinger equation without (AR) condition

In this paper, we are concerned with the existence of least energy nodal solution for the following stationary nonlinear Schrödinger equation(0.1)−Δu(x)+λV(x)u(x)=f(u),x∈RN,N≥3, where λ>0 is a parameter, V has double potential well, and f has asymptotically linear growth or superlinear growth without (AR) condition. By using variational methods, we show that (0.1) has a least energy nodal solution.