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

摘要

In this paper, we are concerned with the existence of least energy solutions of nonlinear Schroedinger equations with electromagnetic fieldsrn-(▽ + iA(x))~2u(x) + (λa(x) + 1)u(x) = ∣u∣~(p-2)u, x ∈ R~nrnfor sufficiently large λ, where i is the imaginary unit, 2 < p < (2N)/(N-2) for N ≥ 3 and 2 < p < + ∞ for N = 1,2. a(x) is a real continuous function on R~N, and A(x) = (A_1 (x), A_2(x),..., A_N(x)) is such that A_j (x) is a real local Hoelder 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 λ large.