Least energy solutions for a weakly coupled fractional Schrödinger system

In this paper, we consider the following system of two weakly coupled fractional nonlinear Schrödinger equations {(−Δ)su+u=(∣u∣2p+b(x)∣u∣p−1∣v∣p+1)ux∈RN(−Δ)sv+ω2sv=(∣v∣2p+b(x)∣v∣p−1∣u∣p+1)vx∈RN. By use of the s-harmonic extension technique, we establish the existence of a nontrivial least energy solution of the system via variational methods. Especially, in the autonomous case i.e. b(x)≡bb(x)≡b, a positive least energy solution with both nontrivial components is obtained.