Nonlinear Schrödinger equation with growing potential on infinite metric graphs. (July 2019) - Akduman, Setenay; Pankov, Alexander
Abstract: The paper deals with nonlinear Schrödinger equations on infinite metric graphs. We assume that the linear potential is infinitely growing. We prove an existence and multiplicity result that covers both self-focusing and defocusing cases. Furthermore, under some additional assumptions we show that solutions obtained bifurcate from trivial ones. We prove that these solutions are superexponentially localized. Our approach is variational and based on generalized Nehari manifold.