Integrodifferential Inclusions In Banach Spaces Research Articles

Optimal Solutions for a Class of Impulsive Differential Problems with Feedback Controls and Volterra-Type Distributed Delay: A Topological Approach

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established for when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied by using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model.

Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents

In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces.

Results on approximate controllability of second-order non-autonomous integrodifferential inclusions via resolvent operators

In this work, we establish a set of sufficient conditions for the approximate controllability for a class of non-autonomous second-order integrodifferential inclusions in Banach spaces. We establish our main results with the help of resolvent operators and Bohnenblust-Karlin's fixed point theorem. Then we extend our study to second-order neutral systems with nonlocal conditions. An example is given to illustrate the main result.

Approximate controllability of neutral integrodifferential inclusions via resolvent operators

In this work, a set of sufficient conditions are established for the approximate controllability for neutral integrodifferential inclusions in Banach spaces. The theory of fractional power and α-norm is used because of the spatial derivatives in the nonlinear term of the system. Bohnenblust-Karlin's fixed point theorem is used to prove our main results. Further, this result is extended to study the approximate controllability for nonlinear functional control system with nonlocal conditions. An example is also given to illustrate our main results.

Controllability results for a class of fractional semilinear integro-differential inclusions via resolvent operators

In this paper, we consider a class of fractional integro-differential inclusions in Banach spaces. This paper deals with the controllability for fractional integro-differential control systems. First, we establishes a set of sufficient conditions for the controllability of fractional semilinear integro-differential inclusions in Banach spaces via resolvent operators. We use Bohnenblust–Karlin’s fixed point theorem to prove our main results. Further, we extend the result to study the controllability concept with nonlocal conditions. An example is also given to illustrate our main results.

On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces

This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by usin

Controllability of mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces

Abstract The paper establishes a sufficient condition for the controllability of semilinear mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces. We use Bohnenblust–Karlin's fixed point theorem combined with a strongly continuous operator semigroup. Our main condition (A5) only depends upon the local properties of multivalued map on a bounded set. An example is also given to illustrate our main results.

Controllability of nonautonomous semilinear integrodifferential inclusions in Banach spaces

In this paper, we establish a sufficient condition for the controllability of nonautonomous integrodifferential inclusions with nonlocal conditions in Banach spaces. The approach used is the Sadovskii’s fixed point theorem with the theory of resolvent operators. Mathematics subject classification (2000): 34A60, 34A37.

Controllability of Second-Order Differential and Integro-Differential Inclusions in Banach Spaces

In this paper, the controllability of second-order differential and integro-differential inclusions in Banach spaces are investigated. Two new results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multivalued maps.

Existence of solutions of Sobolev‐type semilinear mixed integrodifferential inclusions in Banach spaces

The existence of mild solutions of Sobolev‐type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.

Controllability for Functional Differential and Integrodifferential Inclusions in Banach Spaces

In this paper, we establish sufficient conditions for the controllability of functional differential and integrodifferential inclusions in Banach spaces. We rely on a fixed-point theorem for condensing maps due to Martelli.

On Second Order Integrodifferential Inclusions in Banach Spaces

On Second Order Integrodifferential Inclusions in Banach Spaces

Existence results for second order functional differential and integrodifferential inclusions in Banach spaces

In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

Nonlocal Cauchy Problems for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

In this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces with nonlocal conditions. The results are obtained by using a fixed point theorem for condensing maps due to Martelli.

Existence Results on Infinite Intervals for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

Abstract In this paper we investigate the existence of mild solutions, on infinite intervals, to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall rely on the fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem.