Abstract
In this paper, we are concerned with the following semilinear Schrödinger equation with electromagnetic fields and critical growth
for sufficiently large , where
,
and its zero set is not empty,
is the critical Sobolev exponent,
is a constant such that the operator
might be indefinite but is non-degenerate. Using variational method and modified Nehari–Pankov method, we prove the equation admits a least energy solution which localizes near the potential well
. The results we obtain here extend the corresponding results for the Schrödinger equation which involves critical growth but does not involve electromagnetic fields.
Acknowledgements
The authors first want to express their gratitude to the referee and the editor for their valuable comments and suggestions. On the other hand, this paper was finished while the first author visited School of Mathematical Sciences of Beijing Normal University as a visiting fellow. The first author would like to express her gratitude for their hospitality during her visit.
Disclosure statement
No potential conflict of interest was reported by the authors.