Bound states for a coupled Schrodinger system

We consider the existence of bound states for the coupled elliptic system Delta u(1) - lambda(1)u(1) + mu(1)u(1)(3) + beta u(2)(2)u(1) = 0 in R(n), Delta u(2) - lambda(2)u(2) + mu(2)u(2)(3) + beta u(1)(2)u(2) = 0 in R(n), u(1) > 0, u(2) > 0, u(1), u(2) is an element of H(1)(R(n)), where n <= 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum C subset of R(+)(5) x H(1)(R(n)) x H(1)(R(n)) of solutions (lambda(1), lambda(2), mu(1), mu(2), beta, u(1), u(2)) bifurcating from the set of semipositive solutions (where u(1) = 0 or u(2) = 0) and investigate the parameter range covered by C.