A perturbation of nonlinear scalar field equations

In the paper, we consider the following Schrödinger equations −△u+V(x)u=g(u),x∈RN,N≥3,where g satisfies Berestycki-Lions conditions and V is a small perturbation. The assumptions on V are different from the ones in Azzollini and Pomponio (2009). By using the variational methods, we show the equation has a positive ground state solution.