Title Differential equations in abstract spaces / G.E. Ladas and V. Lakshmikantham

Published New York : Academic Press, 1972

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Description 1 online resource (xi, 218 pages) : illustrations Series Mathematics in science and engineering ; v. 85 Mathematics in science and engineering ; v. 85. Contents Front Cover; Differential Equations in Abstract Spaces; Copyright Page; Contents; Preface; Acknowledgments; Chapter 1. The Calculus of Abstract Functions; 1.0 Introduction; 1.1 Abstract Functions; 1.2 The Mean Value Theorem; 1.3 The Riemann Integral Abstract Functions; 1.4 Abstract Lebesgue Integrals; 1.5 The Abstract Stieltjes Integral; 1.6 Gateaux and Fréchet Differentials; 1.7 Notes; Chapter 2. Semigroups of Operators; 2.0 Introduction; 2.1 Strongly Continuous Semigroups of Operators; 2.2 The Infinitesimal Generator; 2.3 The Hille-Yosida-Phillips Theorem 2.4 Linear Autonomous Funtional Differential Equations2.5 Analytic Semigroups; 2.6 Notes; Chapter 3. Linear Evolution Equations of the Parabolic Type: Sobolevski-Tanabe Theory; 3.0 Introduction; 3.1 Definitions and Hypotheses; 3.2 Statements of the Main Theorems and Some Heuristic Arguments; 3.3 Properties of the Semigroup {exo[-tA(t)]}; 3.4 Existence of a Fundamental Solution; 3.5 Uniqueness of the Fundamental Solution; 3.6 Solution of the Abstract Cauchy Problem; 3.7 Differentiability of Solutions; 3.8 Asymptotic Behavior; 3.9 Notes; Chapter 4. Evolution Inequalities; 4.0 Introduction 4.1 Lower Bounds, Uniqueness, and Convexity (Special Results)4.2 Lower Bounds, Uniqueness, and Convexity (General Results); 4.3 Approximate Solutions, Bounds, and Uniqueness; 4.4 Application to Parabolic Equations; 4.5 Notes; Chapter 5. Nonlinear Differential Equations; 5.0 Introduction; 5.1 Counterexamples; 5.2 Existence and Uniqueness; 5.3 Nonlinear Variation of Constants Formula; 5.4 Stability and Asymptotic Behavior; 5.5 Chaplygin's Method; 5.6 Global Existence and Asymptotic Equilibrium; 5.7 Lyapunov Functions and Stability Criteria; 5.8 Notes; Chapter 6. Special Topics; 6.0 Introduction 6.1 Nonlinear Semigroups and Differential Equations6.2 Functional Differential Equations in Banach Spaces; 6.3 Second-Order Evolution Equations; 6.4 Notes; Appendixes; Bibliography; Index Summary Differential equations in abstract spaces Bibliography Includes bibliographical references (pages 211-214) and index Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL English Print version record digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Subject Banach spaces. Differential equations. Nonlinear operators. MATHEMATICS -- Transformations. Banach spaces Differential equations Nonlinear operators Form Electronic book Author Lakshmikantham, V., 1926-2012 ISBN 9780124326507 0124326501 9780080955940 0080955940 1282289152 9781282289154 9786612289156 6612289155

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