Segregated solutions for nonlinear Schrödinger systems with weak interspecies forces

Abstract

We find positive non-radial solutions for a system of Schrödinger equations in a weak fully attractive or repulsive regime in presence of an external radial trapping potential that exhibits a maximum or a minimum at infinity.

2010 Mathematics Subject Classification:

• 35B44 (primary)
• 58C15 (secondary)

Keywords:

• Gross-Pitaevskii systems
• segregated solutions
• spike solutions

Acknowledgement

We would like to thank the referees for their comments and useful advice on our manuscript which substantially helped improving the quality of the paper.

Additional information

Funding

The authors are partially supported by INDAM-GNAMPA funds. A. Pistoia is also partially supported by Fondi di Ateneo “Sapienza” Università di Roma (Italy). G. Vaira is also partially supported by PRIN 2017JPCAPN003 “Qualitative and quantitative aspects of nonlinear PDEs”. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.