Equazioni differenziali astratte: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna (Como), ... Summer Schools, 29) (Italian Edition)

T. Kato: Semi-groups and temporally inhomogeneous evolution equations.- J.L. Lions: Equations différentielles opérationnelles dans les espaces de Hilbert.- L. Nirenberg: Equazioni differenziali ordinarie negli spazi di Banach.- R.S. Phillips: Semi-groups of contraction operators.- L. Amerio: Almost-periodic equations in Hilbert spaces.- G.C. Rota: A limit theorem for the time-dependent evolution equation.- S. Zaidman: Existence and almost periodicity for some differential euqations in Hilbert spaces. Cover ISBN 978-3-642-11003-0 Indice TOSIO KAT0 Semi-Groups and Temporally Inhomogenous Evolution Equations Introduction 1. Generation of Different Types of Semi-Groups 2. The Case in Which -A(t) Are Generators of Analytic Semi-Groups with Constant Domain for A(t)h 3. The Case in Which -A(t) are Generators of Analytic Semi-Groups with Variable Domain 4. The Case in Which -A(t) are Contraction Semi-Groups Bibliography J. L. LIONS Equations Differentielles Operationelles dans les Espaces de Hilbert Chapitre I. Couples D'Espaces Hilbertiens 1. Hypothèses. Exemples 2. L'espace V'. Exemples 3. Une propriete du triplet {V, H, V'} 4. Operateur definipar a(u, v) 5. Une propriete de certains espaces fonctionnels Chapitre II. Equations Lineaires du 1er Ordre 1. Notations. Exemples 2. Le problème. Theoreme d'existence 3. Demonstration du theorème d'existence 2.1 4. Le cas V(t) = V 5. Une application de la methode de transposition Chapitre III. Introduction à Certains Problèmes non Lineaires 1. Position du problème. Generalites 2. Les estimations à priori fondamentales. Applications 3. Le resultat final. Theorème d'existence et d'unicite 4. Cas des Problèmes mixtes Chapitre IV. Equations Lineaires du Deuxième Ordre 1. Position du Problème 2. Proprietes des solutions (eventuelles) de (1.7) 3. Theorème d'existence 4. Proprietes supplementaires de la solution 5. Propriete de dependance continue de la solution en a(t;u, v) et B(t) L. NIRENBERG Equazioni Differenziali Ordinarie Negli Spazi di Banach Capitolo I Introduzione Capitolo 2 Sviluppi in serie di soluzioni esponenziali Capitolo 3 Unicità per il problema di Cauchy e proprietà di convessità Capitolo 4. Stabilità all'infinito Bibliografia R. S. PHILLIPS Semi-Groups of Contraction Operators 1. Introduction 2. Strongly continuous semi-groups of operators 3 - Dissipative operators 4 - The double extension construction 5 - Boundary space theory 6- Operator theory References LUIGI AMERIO Almost-Periodic Equations in Hilbert Spaces GIAN CARLO ROTA A Limit Theorem for the Time-Dependent Evolution Equation 1. Introduction 2. Analytic Preliminaries 3.Main Theorem 4. Applications S. ZAIDMAN Existence and Almost-Periodicity for Some Differential Equations in Hilbert Spaces Bibliography