Least energy solutions for semilinear Schrödinger systems with electromagnetic fields and critical growth

Abstract

In the paper, we study the following semilinear Schrödinger systems with electromagnetic field and critical growth, where , , are real-valued magnetic vector potentials and . and such that , here is the critical Sobolev exponent. are constants such that the operators and are positively definite. We prove the existence of least energy solutions which localize near the common potential well for large enough.

Keywords:

• semilinear Schrödinger systems
• least energy solution
• critical growth
• electromagnetic fields

AMS Subject Classifications:

• 35Q55
• 35J55

Notes

The author was supported by Fundamental Research Funds for the Central Universities and NSFC [grant number 11171028].