On the existence of positive least energy solutions for a coupled Schrodinger system with critical exponent

In this paper, we consider the following coupled Schrodinger system with critical exponent: {-Delta u = lambda u + vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(ss-1)v, x epsilon Omega, -Delta v = mu vertical bar v vertical bar V2*-2+ vertical bar u vertical bar(alpha) vertical bar v vertical bar(ss-1), x epsilon Omega, u, v > 0, x epsilon Omega, u = v = 0, x epsilon partial derivative Omega, where Omega subset of R-N (N >= 3) is a smooth bounded domain, lambda > 0, mu >= 0, and alpha,ss >= 1, alpha + ss = 2* = 2N/N-2. Under certain conditions on lambda and mu, we show that this problem has at least one positive least energy solution. Copyright (C) 2016 John Wiley & Sons, Ltd.