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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.
Acknowledgments
Paper supported by National Science Foundation of China (11061031) and the Fundamental Research Funds for the Gansu University.