Ground states to a quasilinear Schrödinger equation with Berestycki–Lions type nonlinearities

In this paper, we are concerned with the quasilinear Schrödinger equation: −Δu−(κ/2)Δ(u2)u=h(u) in RN ∀u∈H1(RN), where N≥3,κ>0 is a parameter and h satisfies Berestycki–Lions condition. Different from the classical methods, we use a critical point theory on a topological manifold to obtain the existence of a ground state for N≥3, a nonradial ground state solution for N≥4 and infinitely many nonradial solutions for N = 4 or N≥6. Our results generalize several classical works into quasilinear case. Especially, we develop a new computation for building multidimensional paths using a technique of Rk-rearrangement.