Ground state solutions for quasilinear scalar field equations arising in nonlinear optics

In this paper, we study a class of quasilinear elliptic equations which appears in nonlinear optics. By using the mountain pass theorem together with technique adding one dimension space (Hirata et al. Topol Methods Nonlinear Anal 35:253–276, 2010; Jeanjean Theory Appl 28:1633–1659, 1997), prove existence non-trivial weak solution for general terms Berestycki–Lions’ type. The radial ground state and is also established under stronger assumptions on term.