A perturbation of nonlinear scalar field equations. (February 2019) - Liu, Jiu; Liu, Tao; Liao, Jia-Feng
Abstract: In the paper, we consider the following Schrödinger equations − △ u + V ( x ) u = g ( u ), x ∈ R N, 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.