Positive solutions to some systems of coupled nonlinear Schrodinger equations

We study the existence of nontrivial bound state solutions to the following system of coupled nonlinear time-independent Schrodinger equations -Delta u(j) + lambda(j)u(j) = mu(j)u(j)(3) + Sigma(N)(k=1;k not equal j) beta(jk)u(j)u(k)(2), u(j) is an element of W-1,W-2(R-n); j = 1, ... , N where n = 1, 2, 3; lambda(j), mu(j) > 0 for j = 1,..., N, the coupling parameters beta(jk) = beta(kj) is an element of R for j, k = 1,..., N, j not equal k. Precisely, we prove the existence of nonnegative bound state solutions for suitable conditions on the coupling factors. Additionally, with more restrictive conditions on the coupled parameters, weshow that the bound states founded are positive. (C) 2014 Elsevier Ltd.