Existence of solutions for a weakly coupled Schrödinger system with critical growth

In this paper, we are interested in the following critical coupled Schrödinger system: where F(s, t) = sp + tp + λsαtβ, p ∈ (2, 2∗), s, t ≥ 0, α + β = p, s1 > 1, s2 > 1 are two constants satisfying , N ≥ 3. Under some assumptions on the potential functions V, W, K, Q, and for some specific nonlinearities, we are able to prove the existence of purely vector semiclassical solutions that concentrating around some special set characterized by the potentials V, W, K, and Q as ε → 0. Moreover, we also obtain the convergence and exponential decay estimate of these least energy solutions.