MULTIPLE SOLITARY WAVE SOLUTIONS OF NONLINEAR SCHRODINGER SYSTEMS

Consider the N-coupled nonlinear elliptic system (P) {-Delta U-j + U-j = mu U-j(3) + beta U-j Sigma(k not equal j) U-k(2) in Omega, U-j > 0 in Omega, U-j = 0 on partial derivative Omega, j = 1, ... , N. where Omega is a smooth and bounded (or unbounded if Omega is radially symmetric) domain in R-n, n <= 3. By using a Z(N) index theory, we prove the existence of multiple solutions of (P) and show the dependence of multiplicity results on the coupling constant beta.