Existence ground state solutions for a quasilinear Schrodinger equation with Hardy potential and Berestycki-Lions type conditions

In this paper, we discuss the quasilinear Schrodinger equation with a Hardy potential -Delta u + V (x) u - mu u/vertical bar x vertical bar(2) - Delta(u(2)) u = g(u), x is an element of R-N \ {0}, where N >= 3, 0 <= mu < <(mu)over bar>=(N-2)(2)/4, 1/vertical bar x vertical bar(2) is called the Hardy potential. By using Jeanjean's monotonicity trick, we admit a class of ground state solutions for the above problem, under the general Berestycki-Lions type assumptions on the nonlinearity g, as well as some weak assumptions on the potential V. (C) 2021 Elsevier Ltd. All rights reserved.