A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

functionals were discovered and used by volterra over a century ago in his study of the motions of viscous elastic materials and electromagnetic fields. the need to precisely account for the qualitative effects of the cohesion and shape of the domains of these functionals was the major impetus to the development of the branch of mathematics known as topology, and today large numbers of mathemat...

We show that the basic feasible functions of Cook and Urquhart’s BFF [8,9] are precisely the functionals definable in a natural system of ramified recurrence that uses type intersection (for tier-variants of a common type). This further confirms the stability of BFF as a notion of computational feasibility in higher type. It also suggests the potential usefulness of type-intersection restricted...

SIRS models with delay times (discrete or distributed) are studied. By means of Lyapunov functionals, we establish the global stability conditions of the equilibrium states. We will make ingenious linear combination of common quadratic, composite quadratic and Volterra-type functionals, for obtain a suitable Lyapunov functionals.

Complete type Lyapunov Krasovskii functionals for systems with distributed time delays are presented. The derivative of these functionals depends on past states, and they admit a quadratic lower bound. These functionals are suitable for obtaining exponential estimates of the solution and for robustness analysis of uncertain systems Copyright c °2005 IFAC.

employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of neumann two-point boundary valuesturm-liouville type equations. using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.