Multiplicity of Soliton Solutions for Quasilinear Schrödinger Equations

In this paper we use the Fountain theorem to obtain infinitely many solutions for the following class of quasilinear Schr\"{o}dinger equations:\[\begin{array}{lll}-(|u'|^{p-2}u')'+ V(x)|u|^{p-2}u - (|(u^2)'|^{p-2}(u^2)')'u=\lambda|u|^{r-1}u,\ \ u\inW^{1,p}(\mathbb{R}),\\\end{array}\]where $\lambda$ is a positive parameter, $1 < p < \infty, \; r>2p-1 $ and the potential $V(x)$ is nonnegative and bounded away from zero outside of a ball.