Functional Differential Equations In Hilbert Spaces Research Articles

Asymptotic behavior of stochastic functional differential evolution equation

In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a priory uniform in time bounds for the solutions in the appropriate Hilbert spaces. These bounds enable us to establish the existence of invariant measure based on Krylov-Bogoliubov theorem on the tightness of the family of measures. Finally, under certain assumptions on nonlinearities, we establish the uniqueness of invariant measures.

On a class of delay functional-differential equations in Hilbert space

On a class of delay functional-differential equations in Hilbert space

Solubility and properties of solutions of functional-differential equations in Hilbert space

A class of functional-differential equations of neutral type with coefficients that are functions taking values in the set of (in general, unbounded) operators in separable Hilbert space is considered. For such equations results on the well-posed solubility of initial-boundary-value problems on the semiaxis in Sobolev weighted spaces are established.

Structural operators and semigroups associated with functional-differential equations in Hilbert spaces

Structural operators and semigroups associated with functional-differential equations in Hilbert spaces