On the least energy solutions of nonlinear Schrodinger equations with electromagnetic fields

In this paper, we are concerned with the existence of least energy solutions of nonlinear Schrodinger equations with electromagnetic fields -(del + iA(x))(2)u(x) + (lambda a(x) + 1)u(x) = vertical bar u vertical bar(p-2)u, x is an element of R-N for sufficiently large lambda, where i is the imaginary unit, 2 < p < 2N/N-2 for N >= 3 and 2 < p < +infinity for N = 1, 2. a(x) is a real N-2 continuous function on RN, and A(x) = (A(1)(x), A(2)(x), ... , A(N)(x) is such that A(j)(x) is a real local Holder continuous function on R-N for j = 1, 2 ,..., N. Using variational methods we prove the existence of least energy solution u(x) which localizes near the potential well int(a(-1)(0)) for lambda large. (c) 2007 Elsevier Ltd. All rights reserved.