On homotopy Conley index for multivalued flows in Hilbert spaces

An approximation approach is applied to obtain a homotopy version of the Conley type index in Hilbert spaces considered by the first author and W. Kryszewski. The definition given in the paper is more elementary and, as a by-product, gives a natural connection between indices of Kunze and Mrozek in a finite-dimensional case. Some geometric properties of the index from a paper of the second author are discussed in an infinite dimensional situation. Some additional properties for gradient differential inclusions are also presented