Least energy solutions for a non-linear Schrödinger system with electromagnetic fields and potential wells

Abstract

In this paper, we are concerned with the existence of least energy solutions for the following non-linear Schrödinger system with electromagnetic fields(1) for sufficiently large , where is the imaginary unit, and for for is the critical Sobolev exponent. and are real continuous functions on , and are real valued electromagnetic vector potentials with each component are locally Hölder continuous. By using variational methods, we prove the existence of least energy solution of which localizes near the potential well for large enough.