A Morse-Smale index theorem for indefinite elliptic systems and   bifurcation
  We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations. 
Alessandro Portaluri and Nils Waterstraat
math.AP math.DG math.DS math.SG