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A first course in the qualitative theory of differential equations / James Hetao Liu
| A first course in the qualitative theory of differential equations / James Hetao Liu |
| Autore | Liu, James Hetao |
| Pubbl/distr/stampa | Upper Saddle River : Pearson Education, c2003 |
| Descrizione fisica | XVIII, 558 p. : ill. ; 24 cm |
| ISBN | 0-13-008380-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990008015270403321 |
Liu, James Hetao
|
||
| Upper Saddle River : Pearson Education, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topics on stability and periodicity in abstract differential equations [[electronic resource] /] / James H. Liu, Gaston M. N'Guerekata, Nguyen Van Minh
| 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 |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
N'GuerekataGaston M. <1953->
MinhNguyen Van |
| Collana | Series on concrete and applicable mathematics |
| Soggetto topico |
Differential equations - Asymptotic theory
Asymptotic distribution (Probability theory) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-96820-X
9786611968205 981-281-824-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910453278903321 |
|
Liu James Hetao
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topics on stability and periodicity in abstract differential equations [[electronic resource] /] / James H. Liu, Gaston M. N'Guerekata, Nguyen Van Minh
| 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 |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
N'GuerekataGaston M. <1953->
MinhNguyen Van |
| Collana | Series on concrete and applicable mathematics |
| Soggetto topico |
Differential equations - Asymptotic theory
Asymptotic distribution (Probability theory) |
| ISBN |
1-281-96820-X
9786611968205 981-281-824-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910782500003321 |
|
Liu James Hetao
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topics on stability and periodicity in abstract differential equations [[electronic resource] /] / James H. Liu, Gaston M. N'Guerekata, Nguyen Van Minh
| 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 |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
N'GuerekataGaston M. <1953->
MinhNguyen Van |
| Collana | Series on concrete and applicable mathematics |
| Soggetto topico |
Differential equations - Asymptotic theory
Asymptotic distribution (Probability theory) |
| ISBN |
1-281-96820-X
9786611968205 981-281-824-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910825978803321 |
|
Liu James Hetao
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||