LAUSR

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.