Partial Neutral Functional Differential Equations with Infinite Delay : A Contribution to Quantitative and Qualitative Aspects of Study in Infinite Dimension

Hassane Bouzahir

ISBN 10: 3639268113 / ISBN 13: 9783639268119

Edité par VDM Verlag Dr. Müller, 2010

A propos de cet article

nach der Bestellung gedruckt Neuware - Printed after ordering - In this book, we deal with a class of partial (neutral) functional differential equations with infinite delay. We, first, present some results on functional analysis which are useful. We give an axiomatic presentation of the fundamental theory of the phase space and recall some results on integrated semigroups theory. Then, we discuss existence and regularity of solutions in the case where the nonlinear part F is continuous and Lipschitzian with respect to the second variable. After that, we study existence and regularity of solutions in the case where F is locally Lipschitzian. In the case where global existence is verified, we prove that the solution defines a semigroup that satisfies the translation property. This permits us to study stability of an equilibrium point and prove existence of a global attractor. Besides, we give other sufficient conditions for existence and regularity of solutions, and in the autonomous case; we study stability of an equilibrium point. At the end, we investigate existence of periodic solutions in the case where F is periodic in t.

N° de réf. du vendeur 9783639268119

Détails bibliographiques

• Titre: Partial Neutral Functional Differential Equations with Infinite Delay : A Contribution to Quantitative and Qualitative Aspects of Study in Infinite Dimension
• Éditeur: VDM Verlag Dr. Müller
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 3639268113
• ISBN à 13 chiffres: 9783639268119
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 22 L x 15 H x 0,7 P (centimètres) 22 centimètres de largeur par 15 centimètres de hauteur par 0,7 centimètres de profondeur
• Poids: 201 grammes

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Synopsis

In this book, we deal with a class of partial (neutral) functional differential equations with infinite delay. We, first, present some results on functional analysis which are useful. We give an axiomatic presentation of the fundamental theory of the phase space and recall some results on integrated semigroups theory. Then, we discuss existence and regularity of solutions in the case where the nonlinear part F is continuous and Lipschitzian with respect to the second variable. After that, we study existence and regularity of solutions in the case where F is locally Lipschitzian. In the case where global existence is verified, we prove that the solution defines a semigroup that satisfies the translation property. This permits us to study stability of an equilibrium point and prove existence of a global attractor. Besides, we give other sufficient conditions for existence and regularity of solutions, and in the autonomous case; we study stability of an equilibrium point. At the end, we investigate existence of periodic solutions in the case where F is periodic in t.