Xianlong Fu

Existence of solutions for neutral functional differential evolution equations with nonlocal conditions

Abstract In this paper, by using fractional power of operators and Sadovskiis fixed point theorem, we study the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions. The results we obtained are a generalization and continuation of the recent results on this issue. In the end, an example is given to show the application of our results.

Existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions

Abstract In this work, we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions. We assume that the linear part generates a strongly continuous semigroup on a general Banach space.

Controllability of neutral functional differential systems in abstract space

In this paper, by using fractional power of operators and Sadovskii fixed point theorem, we study the controllability and the local controllability of abstract neutral functional differential systems with unbounded delay. As application, an example is provided to illustrate the obtained results.

Controllability of abstract neutral functional differential systems with unbounded delay

In this paper, by using Sadovskii fixed point theorem, we study the controllability and the local controllability of abstract neutral functional differential systems with unbounded delay. As application, an example is provided to illustrate the obtained results.

Controllability of non-densely defined functional differential systems in abstract space ☆

Abstract In this work, with the Schauder fixed point theorem applied, we establish a result concerning the controllability for a class of abstract functional differential systems where the linear part is non-densely defined and satisfies the Hille–Yosida condition. As an application, an example is provided to illustrate the result obtained.

Existence of solutions for neutral integro-differential equations with state-dependent delay

In this paper, we study the existence and regularity of solutions for a neutral functional integro-differential equation with state-dependent delay in Banach space. The mild solutions are investigated by Sadovskii fixed point theorem under compactness condition for the resolvent operator, and the theory of fractional power and @a-norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives. The strict solutions are obtained under Holder continuity condition. Hence this work extends and develops the existed results on this topic. In the end an example is provided to illustrate the application of the obtained results.

Approximate controllability of semi-linear neutral integro-differential systems with finite delay

Abstract This paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in Hilbert space. Since the considered equation admits nonlinear terms involving spatial derivatives, the fraction power theory and α -norm are used to discuss the problem so that the established results can be applied to them. The results are obtained by using the Sadovskii fixed point theorem and the theory of analytic resolvent operator. An example is presented to illustrate the applications of the obtained results.

Controllability of neutral functional integrodifferential systems in abstract space

In this paper, by using fractional power of operators and Sadovskii fixed point theorem, we study the controllability of abstract neutral functional integrodifferential systems with infinite delay. As application, an example is provided to illustrate the obtained results.

Periodic solutions for differential equations at resonance with unbounded nonlinearities

Abstract In this paper, sufficient conditions are given for the existence of periodic solutions of nonlinear coupled differential systems and Duffing equations at resonance with unbounded nonlinearities. Also, two examples are offered to show the applications of the obtained results.