Kneser's theorem for multivalued differential delay equations
Pavel Krbec, Jaroslav Kurzweil (1979)
Časopis pro pěstování matematiky
Dan Goreac, Oana-Silvia Serea (2012)
ESAIM: Control, Optimisation and Calculus of Variations
The aim of the paper is to provide a linearization approach to the -control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the approach and the associated linear formulations. This seems to be the most appropriate tool for treating problems in continuous and lower semicontinuous setting.
Dan Goreac, Oana-Silvia Serea (2012)
ESAIM: Control, Optimisation and Calculus of Variations
The aim of the paper is to provide a linearization approach to the See PDF-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating See PDF problems in continuous and lower semicontinuous...
Wolfgang Desch (1998)
Applications of Mathematics
On a closed convex set in with sufficiently smooth () boundary, the stop operator is locally Lipschitz continuous from into . The smoothness of the boundary is essential: A counterexample shows that -smoothness is not sufficient.
Tzanko Donchev (1998)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
In the paper we consider lower semicontinuous differential inclusions with one sided Lipschitz and compact valued right hand side in a Banach space with uniformly convex dual. We examine the nonemptiness and some qualitative properties of the solution set.
Tzanko Donchev (1998)
Colloquium Mathematicae
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.
Donchev, Tzanko, Ivanov, Radostin (2001)
Novi Sad Journal of Mathematics
Laghdir, M., Monteiro Marques, Manuel D.P. (1997)
Journal of Convex Analysis
Teresa Janiak, Elżbieta Łuczak-Kumorek (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧ (0) ⎨ ⎩ (1)
Azzam-Laouir, D. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Tzanko Donchev (2001)
Annales Polonici Mathematici
We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.
Dhage, Bapurao C. (2006)
Applied Mathematics E-Notes [electronic only]
Malaguti, Luisa (1996)
Journal of Convex Analysis
Mirică, Ştefan (2004)
International Journal of Mathematics and Mathematical Sciences
L. Paoli, M. Schatzman (1993)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
M. Benchora, S. K. Ntouyas (2001)
Matematički Vesnik
Bapur Chandra Dhage (2004)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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.
Filippakis, Michael E., Papageorgiou, Nikolaos S. (2004)
Fixed Point Theory and Applications [electronic only]
Ntouyas, Sotiris K. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
M. Benchohra, S. K. Ntouyas (2001)
Bollettino dell'Unione Matematica Italiana
In questo lavoro studiamo l'esistenza di soluzioni deboli su un intervallo compatto di problemi con valore iniziale per inclusioni funzionali neutre differenziali e integrodifferenziali in spazi di Banach. I risultati sono ottenuti usando un teorema di punto fisso per mappe condensanti dovuto a Martelli.