LEADER 05490nam 2200697Ia 450 001 9910825978803321 005 20240313221930.0 010 $a1-281-96820-X 010 $a9786611968205 010 $a981-281-824-3 035 $a(CKB)1000000000554625 035 $a(EBL)1193248 035 $a(SSID)ssj0000311676 035 $a(PQKBManifestationID)12083459 035 $a(PQKBTitleCode)TC0000311676 035 $a(PQKBWorkID)10328817 035 $a(PQKB)11444891 035 $a(MiAaPQ)EBC1193248 035 $a(WSP)00006870 035 $a(Au-PeEL)EBL1193248 035 $a(CaPaEBR)ebr10688067 035 $a(CaONFJC)MIL196820 035 $a(OCoLC)318879612 035 $a(EXLCZ)991000000000554625 100 $a20081027d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTopics on stability and periodicity in abstract differential equations /$fJames H. Liu, Gaston M. N'Guerekata, Nguyen Van Minh 205 $a1st ed. 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2008 215 $a1 online resource (220 p.) 225 1 $aSeries on concrete and applicable mathematics ;$vv. 6 300 $aDescription based upon print version of record. 311 $a981-281-823-5 320 $aIncludes bibliographical references (p. 201-206) and index. 327 $aContents; 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 327 $a1.3.4.1 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 327 $a3.1.3 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 327 $a3.2.2 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 327 $a4.2 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 327 $a5. Nonlinear equations 330 $aThis book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas. 410 0$aSeries on concrete and applicable mathematics ;$vv. 6. 606 $aDifferential equations$xAsymptotic theory 606 $aAsymptotic distribution (Probability theory) 615 0$aDifferential equations$xAsymptotic theory. 615 0$aAsymptotic distribution (Probability theory) 676 $a515/.35 700 $aLiu$b James Hetao$0285715 701 $aN'Guerekata$b Gaston M.$f1953-$0911958 701 $aMinh$b Nguyen Van$01637043 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910825978803321 996 $aTopics on stability and periodicity in abstract differential equations$93978618 997 $aUNINA