Existence and multiplicity of positive solutions for two coupled nonlinear Schrödinger equations
Journal
Discrete and Continuous Dynamical Systems- Series A
Journal Volume
33
Journal Issue
7
Pages
2911-2938
Date Issued
2013
Author(s)
Wu, T.-F.
Abstract
It is well known that a single nonlinear Schrödinger (NLS) equation with a potential V and a small parameter ε may have a unique positive solution that is concentrated at the nondegenerate minimum point of V . However, the uniqueness may fail for two-component systems of NLS equations with a small parameter ε and potentials V1 and V2 having the same nondegenerate minimum point. In this paper, we will use energy estimates and category theory to prove the nonuniqueness theorem.
SDGs
Type
journal article