In this paper, we study the existence of positive solutions to the following Schrodinger system: where N = 1; 2; 3; V_1(x) and V_2(x) are positive and continuous, but may not be well-shaped; and μ_1(x), μ_2(x) and β(x) are continuous, but may not be positive or anti-well-shaped. We prove that the system has a positive solution when the coefficients V_i(x), μ_i(x) (i = 1...
