Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay

We consider an impulsive neutral fractional integrodifferential equation with infinite delay in an arbitrary Banach spaceX. The existence of mild solution is established by using solution operator and Hausdorff measure of noncompactness.

On the Existence and Uniqueness of a Solution to a Stochastic Differential Equation in a Banach Space

Abstarct A sufficient condition is given for the existence of a solution to a stochastic differential equation in an arbitrary Banach space. The method is based on the concept of covariance operator and a special construction of the Itô stochastic integral in an arbitrary Banach space.

Integrodifferential equations with analytic semigroups

In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

Regular multilinear operators on C(K) spaces

The purpose of this paper is to characterise the class of regular continuous multilinear operators on a product of C(K) spaces, with values in an arbitrary Banach space. This class has been considered recently by several authors in connection with problems of factorisation of polynomials and holomorphic mappings. We also obtain several characterisations of a compact dispersed space K in terms of polynomials and multilinear forms defined on C(K).

Semilinear integro-differential equations with compact semigroups

In this paper we study the local and global existence of mild solutions to a class of integro-differential equations in an arbitrary Banach space associated with the operators generating compact semigroups on the Banach space.