Synopses & Reviews
This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.
Table of Contents
Preface. Notation.
I: Scalar Linear Integral Inequalities. 1. Gronwall-Type Inequalities.
2. Inequalities of the Type of Chu and Metcalf.
3. Applications
I: Notes and Comments.
II: Scalar Nonlinear Integral Inequalities. 4. Integral Inequalities Investigated by Nonstandard Methods.
5. Bihari-Type Inequalities.
6. Comparison Results.
7. Lakshmikantham's Comparison Method.
8. Inequalities of the Type of Deo and Dhongade.
9. Applications.
II: Notes and Comments.
III: Analogues of Gronwall's Inequality. 10. Integral Inequalities Involving Several Integrals.
11. Integral Inequalities with Iterated Integrals.
12. Integral Inequalities with Iterated Integrals.
12. Integral Inequalities for Functions of
N Variables.
13. Integro-Differential Inequalities.
14. Integral Inequalities with Delay.
15. Discrete Inequalities.
16. Impulse Integral Inequalities.
17. Inequalities Involving Stieltjes Integrals.
18. Systems of Integral Inequalities.
19. Inequalities in Partially Ordered Spaces.
20. Applications.
III: Notes and Comments. Bibliography. Index (of Authors). Index.