### On homotopy Conley index for multivalued flows in Hilbert spaces

#### Abstract

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.

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.

#### Keywords

Conley index; multivalued dynamical system

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