Existence And Asymptotic Behavior Of Ground State For Semi-classical Hartree Type Schr?dinger Equations

In this paper,we are concerned with the existence of ground-state solution for the two-component Hartree equations with potentials (?)By virtue of the the compact embedding of the weighted Sobolev space and the concentration-compactness method respectively,we obtain the existence of ground state solutions under the cases that when |x| → +∞,the external potential V_j(x)→+∞ or V_j(x)<+∞(j=1,2).Furthermore,as ε→ 0,we present the energy estimates and the decay rate for the ground state solution.We also give a discussion to show the interaction between the components is attractive or repulsive.