Nonradial symmetric bound states for a system of coupled Schrödinger equations
Juncheng Wei
University of British Columbia, Vancouver, CanadaTobias Weth
Universität Giessen, Germany

Abstract
We consider bound state solutions of the coupled elliptic system
\[ \Delta u - u + u^3 +\beta v^2 u=0 \ \mbox{in} \ \R^N, \] \[ \Delta v - v + v^3 +\beta u^2 v=0 \ \mbox{in} \ \R^N, \]where . It is known (\cite{lw1}) that when , there are no ground states, i.e., no least energy solutions. We show that, for certain finite subgroups of acting on , least energy solutions can be found within the associated subspaces of symmetric functions. For these solutions are nonradial. From this we deduce, for every , the existence of infinitely many nonradial bound states of the system.
Cite this article
Juncheng Wei, Tobias Weth, Nonradial symmetric bound states for a system of coupled Schrödinger equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 279–294
DOI 10.4171/RLM/495