Please see manuscript PDF for full abstract with equations.
We consider the following semiclassical generalized quasilinear Schr\"{o}dinger equation\begin{equation*}-\varepsilon^2\text{div} (g^2(v)\nabla v)+\varepsilon^2g(v)g'(v)|\nabla v|^2+V(x)v=f(v), \quad x\in \mathbb{R}^{N},\end{equation*} where $V\in C^1(\mathbb{R}^N)$ is bounded and $f$ is odd in $v$ and satisfies a monotonicity condition. We establish the existence of multiple localized solutions concentrating at the set of critical points of $V$.