Differential and integral inequalities [electronic resource] : theory and applications. Volume II / V. Lakshmikantham and S. Leela.

Format:

Book

Author/Creator:

Lakshmikantham, V., 1926-

Contributor:

Leela, S.

Series:

Mathematics in science and engineering ; v. 55B.

Mathematics in science and engineering ; 55B

Language:

English

Subjects (All):

Differential equations.

Integral equations.

Differential inequalities.

Inequalities (Mathematics).

Physical Description:

1 online resource (335 p.)

Place of Publication:

New York : Academic Press, 1969.

Language Note:

English

Summary:

Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations

Contents:

Front Cover; Differential and Integral Inequalities; Copyright Page; Preface; Contents; PART 1: FUNCTIONAL DIFFERENTIAL EQUATIONS; Chapter 6; 6.0 Introduction; 6.1 Existence; 6.2 Approximate Solutions and Uniqueness; 6.3 Upper Bounds; 6.4 Dependence on Initial Values and Parameters; 6.5 Stability Criteria; 6.6 Asymptotic Behavior; 6.7 A Topological Principle; 6.8 Systems with Repulsive Forces; 6.9 Functional Differential Inequalities; 6.10 Notes; Chapter 7; 7.0 Introduction; 7.1 Stability Criteria; 7.2 Converse Theorems; 7.3 Autonomous Systems; 7.4 Perturbed Systems; 7.5 Extreme Stability

7.6 Almost Periodic Systems7.7 Notes; Chapter 8; 8.0 Introduction; 8.1 Basic Comparison Theorems; 8.2 Stability Criteria; 8.3 Perturbed Systems; 8.4 An Estimate of Time Lag; 8.5 Eventual Stability; 8.6 Asymptotic Behavior; 8.7 Notes; PART 2: PARTIAL DIFFERENTIAL EQUATIONS; Chapter 9; 9.0 Introduction; 9.1 Partial Differential Inequalities of First Order; 9.2 Comparison Theorems; 9.3 Upper Bounds; 9.4 Approximate Solutions and Uniqueness; 9.5 Systems of Partial Differential Inequalities of First Order; 9.6 Lyapunov-Like Function; 9.7 Notes; Chapter 10; 10.0 lntroduction

10.1 Parabolic Differential Inequaliies in Bounded Domains10.2 Comparison Theorems; 10.3 Bounds, Under and Over Functions; 10.4 Approximate Solutions and Uniqueness; 10.5 Stability of Steady-State Solutions; 10.6 Systems of Parabolic Differential inequalities in Bounded Domains; 10.7 Lyapunov-Like Functions; 10.8 Stahility and Boundedness; 10.9 Conditional Stability and Boundedness; 10.10 Parabolic Differential Inequalities in Unbounded Domains; 10.11 Uniqueness; 10.12 Exterior Boundary-Value Problem and Uniqueness; 10.13 Notes; Chapter 11; 11.0 Introduction

11.1 Hyperbolic Diflerential Inequalities11.2 Uniqueness Criteria; 11.3 Upper Bounds and Error Estimates; 11.4 Notes; PART 3: DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES; Chapter 12; 12.0 Introduction; 12.1 Existence; 12.2 Nonlocal Existence; 12.3 Uniqueness; 12.4 Continuous Dependence and the Method of Averaging; 12.5 Existence (continued); 12.6 Approximate Solutions and Uniqueness; 12.7 Chaplygin's Method; 12.8 Asymptotic Behavior; 12.9 Lyapunov Function and Comparison Theorems; 12.10 Stability and Boundedness; 12.11 Notes; PART 4: COMPLEX DIFFERENTIAL EQUATIONS; Chapter 13; 13.0 Introduction

13.1 Existence, Approximate Solutions, and Uniqueness13.2 Singularity-Free Regions and Growth Estimates; 13.3 Componentwise Bounds; 13.4 Lyapunov-like Functions and Comparison Theorems; 13.5 Notes; Bibliography; Author Index; Subject Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28912-8

9786612289125

0-08-095564-9

OCLC:

428095233