Solution semigroup and invariant manifolds for functional equations with infinite delay

Research Article Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the non...

Semilinear functional difference equations with infinite delay

We obtain boundness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications on Volterra difference equations with infinite delay are shown.

Existence of Invariant Manifolds for Stochastic Equations in Infinite Dimension

We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk [5]. We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor [16]. Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application we char...

Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay

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Local Existence of the Solution for Stochastic Functional Differential Equations with Infinite Delay