Multi-bump bound state solutions for the quasilinear Schrödinger equation with critical frequency (Q461297)

The paper addresses multidimensional generalized nonlinear Schrödinger equations for a function \(u\) in spaces of dimension \(\geq 3\), with the usual subcritical nonlinear term, an external potential, and an additional nonlinear term of type \(\nabla^2(|u|^2)u\). The aim of the work is to rigorously prove that the external potential with a single or several local potential wells gives rise to a ground state with, respectively, one or several local density peaks. The proof is performed in functional spaces of the Orlicz type.