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Let be a bounded domain in R N with smooth boundary. Consider the u = @vH(u;v;x) in , v = @uH(u;v;x) in , u = 0; v = 0 in @ . We assume that H is an even \ "-type Hamiltonian function whose rst order partial derivatives satisfy appropriate growth conditions. We show that if (0; 0) is a hyperbolic solution of (ES), then (ES) has at least 2j j nontrivial solutions, where = (0; 0) is the renormalized Morse index of (0; 0). This proves a conjecture by Angenent and van der Vorst.

Multiple solutions of indefinite elliptic systems via a Galerkin-type Conley index theory