Topics on stability and periodicity in abstract differential equations [[electronic resource] /] / James H. Liu, Gaston M. N'Guerekata, Nguyen Van Minh

• Autore: Liu James Hetao
• Pubblicazione: Singapore ; ; Hackensack, NJ, : World Scientific, c2008
• Descrizione fisica: 1 online resource (220 p.)
• Disciplina: 515/.35
• Soggetto topico: Differential equations - Asymptotic theory; Asymptotic distribution (Probability theory)
• Altri autori: N'GuerekataGaston M. <1953-> MinhNguyen Van
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 201-206) and index.
• Nota di contenuto: Contents; Preface; 1. Preliminaries; 1.1 Banach Spaces and Linear Operators; 1.1.1 Banach Spaces; 1.1.2 Linear Operators; 1.1.3 Spectral Theory of Linear (Closed) Operators; 1.1.3.1 Several Properties of Resolvents; 1.2 Strongly Continuous Semigroups of Operators; 1.2.1 Definition and Basic Properties; 1.2.2 Compact Semigroups and Analytic Strongly Continuous Semigroups; 1.2.3 Spectral Mapping Theorems; 1.2.4 Commuting Operators; 1.3 Spectral Theory; 1.3.1 Introduction; 1.3.2 Spectrum of a Bounded Function; 1.3.3 Uniform Spectrum of a Bounded Function; 1.3.4 Almost Periodic Functions ; 1.3.4.1 De nition and basic properties1.3.5 Sprectrum of an Almost Periodic Function; 1.3.6 A Spectral Criterion for Almost Periodicity of a Function; 1.3.7 Almost Automorphic Functions; 2. Stability and Exponential Dichotomy; 2.1 Perron Theorem; 2.2 Evolution Semigroups and Perron Theorem; 2.3 Stability Theory; 2.3.1 Exponential Stability; 2.3.2 Strong Stability; 2.4 Comments and Further Reading Guide; 2.4.1 Further Reading Guide; 2.4.2 Comments; 3. Almost Periodic Solutions; 3.1 Evolution Semigroups & Periodic Equations; 3.1.1 An Example; 3.1.2 Evolution Semigroups ; 3.1.3 The Finite Dimensional Case3.1.4 The Infinite Demensional Case; 3.1.5 Almost Periodic Solutions and Applications; 3.1.5.1 Invariant functions spaces of evolution semigroups; 3.1.5.2 Monodromy operators; 3.1.5.3 Unique solvability of the inhomogeneous equations in P(1); 3.1.5.4 Unique solvability in AP(X) and exponential dichotomy; 3.1.5.5 Unique solvability of the inhomogeneous equations in M(f); 3.1.5.6 Unique solvability of nonlinearly perturbed equations; 3.1.5.7 Example 1; 3.1.5.8 Example 2; 3.2 Sums of Commuting operators; 3.2.1 Invariant Function Spaces ; 3.2.2 Differential Operator d/dt - A and Notions of Admissibility3.2.3 Admissibility for Abstract Ordinary Differential Equations; 3.2.4 Higher Order Differential Equations; 3.2.5 Abstract Functional Differential Equations; 3.2.6 Examples and Applications; 3.3 Decomposition Theorem; 3.3.1 Spectral Decomposition; 3.3.2 Spectral Criteria For Almost Periodic Solutions; 3.4 Comments and Further Reading Guide; 3.4.1 Further Reading Guide; 3.4.2 Comments; 4. Almost Automorphic Solutions; 4.1 The Inhomogeneous Linear Equation ; 4.2 Method of Invariant Subspaces and Almost Automorphic Solutions of Second-Order Differential Equations4.3 Existence of Almost Automorphic Solutions to Semilinear Differential Equations; 4.4 Method of Sums of Commuting Operators and Almost Automorphic Functions; 4.5 Almost Automorphic Solutions of Second Order Evolution Equations; 4.5.1 Mild Solutions of Inhomogeneous Second Order Equations; 4.5.1.1 Mild Solutions; 4.5.1.2 Mild Solutions and Weak solutions; 4.5.2 Operators A; 4.5.3 Nonlinear Equations; 4.6 The Equations x'=f(t,x); 4.7 Comments and Further Reading Guide ; 5. Nonlinear equations
• Sommario/riassunto: This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.
• Titolo autorizzato: Topics on stability and periodicity in abstract differential equations
• ISBN: 1-281-96820-X; 9786611968205; 981-281-824-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910825978803321
• Lo trovi qui: Univ. Federico II
• Serie: Series on concrete and applicable mathematics ; ; v. 6.