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摘要
In this paper, we are concerned with the following nonlinear Schrodinger system with electromagnetic fields {-(del + iA(x))(2)u(x) + lambda V(x)u(x) = 2 alpha/alpha+beta vertical bar u(x)vertical bar(alpha-2)vertical bar v(x)vertical bar(beta)u(x), x is an element of R-N , -(del + iB(x))(2)v(x) + lambda W(x)v(x) = 2 beta/alpha+beta vertical bar u(x)vertical bar(alpha)vertical bar v(x)vertical bar(beta-2)v(x), x is an element of R-N , ((S lambda)) vertical bar u(x)vertical bar -> 0, vertical bar v(x)vertical bar -> 0 as vertical bar x vertical bar -> infinity for sufficiently large lambda, where i is the imaginary unit, alpha > 1, beta > 1, alpha + beta < Theta and Theta = 2N/N-2 for N >= 3, Theta = +infinity for N = 1, 2. A(x) and B(x) are real-valued electromagnetic vector potentials. V(x) and W(x) are real-valued continuous nonnegative functions on R-N. By modifying the nonlinearity and using the decay flow we show that if Omega := int V-1(0) boolean AND int W-1(0) has several isolated connected components Omega(1), Omega(2), ...., Omega(k) such that the interior Omega(i) is not empty and partial derivative Omega(i), is smooth for all i epsilon {1, 2, ... , k}, then for any non-empty subset J (1, 2, ... , k) there exists a solution (u lambda., u lambda) of (S-lambda) for lambda > 0 large. Moreover for any sequence lambda(n) -> infinity, up to a subsequence (u lambda(n), u lambda(n)) converges in Omega(i) (j epsilon j) to a least energy solution of the following limit problem {-(del + iA(x))(2) u(x) = 2 alpha/alpha+beta vertical bar u(x)vertical bar(alpha-2)vertical bar v(x)vertical bar(beta)u(x), x is an element of Omega(j), -(del + iB(x))(2) v(x) = 2 beta/alpha+beta vertical bar u(x)vertical bar(alpha)vertical bar v(x)vertical bar(beta-2)v(x), x is an element of Omega(j), ((D Omega j)) (u(x), v(x)) epsilon 0 as H-A,B(0.1) (Omega(j)) and outside of boolean OR(j is an element of J) (Omega j) to (0,0).
