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

By introducing some new tricks, we prove that the following generalized quasilinear Schrodinger equation -div (g(2)(u)del u) + g(u)g'(u)vertical bar del u vertical bar(2) + V(x)u = f(u), x is an element of R-N 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. Published by AIP Publishing.