A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology

We study critical points of the indefinite functional f(H)(u, v) = integral{del u . del v - H(x, u, v)}dx by applying Fleer's homology construction to the ordinary gradient flow of the functional f on a suitable Sobolev space. One of our main observations is that even though this flow is well posed in both time directions and lacks any kind of smoothing property one can still obtain compactness of connecting orbit spaces and thus define the Fleer homology for f(H).