Ground state solutions for generalized quasilinear Schrödinger equations with variable potentials and Berestycki-Lions nonlinearities

By introducing some new tricks, we prove that the following generalized quasilinear Schrödinger equation −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(u), x∈RN admits two classes of ground state solutions under the general “Berestycki-Lions assumptions” on the nonlinearity f which are almost necessary conditions, as well as some weak assumptions on the potential V. Moreover, we also give a minimax characterization of the ground state energy. Our results improve and complement the previous ones in the literature.