Neutral Functional Evolution Equations Research Articles

Nonlocal controllability of mild solutions for neutral evolution equations with state-dependent delay in Fréchet spaces

In this paper, we prove the controllability of mild solutions of neutral functional evolution equations with state-dependent delay and nonlocal conditions. We establish the non local controllability of mild solutions under certain conditions by combining Avramescu’s nonlinear alternative for the sum of compact and contraction operators in Fréchet spaces with semigroup theory.

Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

AbstractIn this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.

Controllability of Second‐Order Semilinear Impulsive Stochastic Neutral Functional Evolution Equations

We consider a class of impulsive neutral second‐order stochastic functional evolution equations. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. An example is provided to illustrate our results.

EXISTENCE OF SOLUTIONS FOR DOUBLE PERTURBED IMPULSIVE NEUTRAL FUNCTIONAL EVOLUTION EQUATIONS

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

Global uniqueness results for partial functional and neutral functional evolution equations with infinite delay

In this paper, we provide sufficient conditions for the existence of a unique mild solution on a semi-infinite interval for two classes of first-order partial functional and neutral functional differential evolution equations with infinite delay using a recent nonlinear alternative of Leray Schauder type due to Frigon and Granas for contractions maps in Fréchet spaces, combined with semigroup theory.

Controllability for Semilinear Functional and Neutral Functional Evolution Equations with Infinite Delay in Fréchet Spaces

The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Frechet spaces, combined with the semigroup theory.

Existence of periodic solutions for abstract neutral non-autonomous equations with infinite delay

In this paper, by using Sadovskii fixed point theorem, we study the existence of solutions and periodic solutions for a class of abstract neutral functional evolution equations with infinite delay. An example is presented in the end to show the applications of the obtained results.