Multiple solutions for a quasilinear Schrödinger equation

Abstract

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,...,xN and g is odd in u, subcritical and satisfies a monotonicity condition. We employ the approach developed in Szulkin and Weth (2009, 2010) [15,16] and obtain infinitely many geometrically distinct solutions. © 2012 Elsevier Inc.