Sign-changing solutions for coupled nonlinear Schrodinger equations with critical growth

We consider the following nonlinear Schrodinger system with critical growth -Delta u(j) = lambda(j)u(j) + Sigma(k)(i=1) beta(ij)vertical bar u(i)vertical bar(2*/2) vertical bar u(j)vertical bar(2*/2)u(j), in Omega, u(j) = 0, on partial derivative Omega, j = 1, ... ,k, where Omega is a bounded smooth domain in R-N, 2* = 2N/N-2, 0 < lambda(j) < lambda(1) (Omega), j = 1, ... , k, lambda(1) (Omega) is the first eigenvalue of -Delta with zero Dirichlet boundary condition. We consider the repulsive case, namely beta(jj) > 0, j = 1, ..., k, beta(ij) = beta(ji) <= 0, i not equal j, i, j = 1, ... , k. The existence of infinitely many sign-changing solutions as bound states is proved, provided N >= 7, by approximations of systems with subcritical growth and by the concentration analysis on approximating solutions. (C) 2016 Elsevier Inc. All rights reserved.