A Riesz type integral representation theorem of comonotonically additive functionals

Integral Representation of Continuous Comonotonically Additive Functionals

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...

The Riesz representation theorem

Integral Representation of Abstract Functionals of Autonomous Type

In this work we extend the results of [2] to a family of abstract functionals of autonomous type satisfying suitable locality and additivity properties, and general integral growth conditions of superlinear type. We single out a condition which is necessary and sufficient in order for a functional of this class to admit an integral representation, and sufficient as well to have an integral repr...

A bifurcation theorem for noncoercive integral functionals

In this paper we study the existence of critical points for noncoercive functionals, whose principal part has a degenerate coerciveness. A bifurcation result at zero for the associated differential operator is established.

Representation of additive and biadditive functionals