Multiple solutions for a quasilinear Schrödinger equation

In this paper we consider the quasilinear Schrödinger equation−Δu+V(x)u−Δ(u2)u=g(x,u),x∈RN, where g and V   are periodic in x1,…,xNx1,…,xN and g is odd in u, subcritical and satisfies a monotonicity condition. We employ the approach developed in Szulkin and Weth (2009, 2010) [15] and [16] and obtain infinitely many geometrically distinct solutions.