Standing waves for quasilinear Schröinger equations with indefinite potentials

Shibo Liu, Jian Zhou

We consider quasilinear Schrödinger equations in ${\mathbb{R}}^N$ of the form% \[ -Δu+V(x)u-uΔ(u^{2})=g(u)\text{,}% \] where $g(u)$ is $4$-superlinear. Unlike all known results in…