The cohomological span of LS-Conley index

In this paper we introduce a new homotopy invariant - the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula for the LS-index of an isolated critical point, which is an extension of the classical Dancer theorem for the case of LS-index.