Nonradial solutions of quasilinear Schrödinger equations with general nonlinearity.

Consider the quasilinear Schrödinger equation$ -\Delta u+V(x)u-\frac12 \Delta(u^2)u = h(u)+\mu l(u),\ \ u\in H^1({\mathbb{R}}^N), $where $ V(x) $ is a radial potential allowed to be singular at $ x = 0 $, $ h $ is an odd nonlinearity of the Berestycki-Lions type, $ \mu\in{\mathbb{R}} $ is a small parameter and $ l $ is a general odd function. While most works in the literature are restricted to radial solutions, we develop a new variational approach to derive the existence of multiple nonradial solutions by proposing a nonlocal perturbation process. [ABSTRACT FROM AUTHOR]