Displaying similar documents to “Mixed type semicontinuous differential inclusions in Banach spaces”

Second-order viability result in Banach spaces

Myelkebir Aitalioubrahim, Said Sajid (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.

The method of upper and lower solutions for perturbed nth order differential inclusions

Bupurao C. Dhage, Adrian Petruşel (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].

Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

N.U. Ahmed (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.

Multi-valued operators and fixed point theorems in Banach algebras

Bapur Chandra Dhage (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper, two multi-valued versions of the well-known hybrid fixed point theorem of Dhage [6] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is also proved under the mixed Lipschitz and compactness type conditions.

Lower semicontinuous differential inclusions. One-sided Lipschitz approach

Tzanko Donchev (1998)

Colloquium Mathematicae

Similarity:

Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.