Foundations of Iso-Differential Calculus. Volume 3: Ordinary Iso-Differential Equations

Svetlin G. Georgiev
Sorbonne University, Paris, France
Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

Series: Mathematics Research Developments
BISAC: MAT005000

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This book is intended for readers who have had a course in iso-differential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with exact iso-differential equations, while first-order iso-differential equations are studied in Chapter 2 and Chapter 3. Chapter 4 discusses iso-integral inequalities. Many iso-differential equations cannot be solved as finite combinations of elementary functions. Therefore, it is important to know whether a given iso-differential equation has a solution and if it is unique. These aspects of the existence and uniqueness of the solutions for first-order initial value problems are considered in Chapter 5. Iso-differential inequalities are discussed in Chapter 6.

Continuity and differentiability of solutions with respect to initial conditions are examined in Chapter 7. Chapter 8 extends existence-uniqueness results and continuous dependence on initial data for linear iso-differential systems. Basic properties of solutions of linear iso-differential systems are given in Chapter 9. Chapter 10 deals with the fundamental matrix solutions. In Chapter 11, necessary and sufficient conditions are provided so that a linear iso-differential system has only periodic solutions. The asymptotic behaviour of the solutions of linear systems is investigated in Chapter 12. Chapters 13 and 14 are devoted to some aspects of the stability of solutions of iso-differential systems. The last major topic covered in this book is that of boundary value problems involving second-order iso-differential equations. After linear boundary value problems are introduced in Chapter 15, Green’s function and its construction is discussed in Chapter 16.
(Imprint: Nova)

Preface

Chapter 1 - Exact Equations (pp. 1-48)

Chapter 2 - Elementary First-Order Equations (pp. 49-72)

Chapter 3 - First-Order Linear Equations (pp. 73-100)

Chapter 4 - Iso-Integral Inequalities (pp. 101-110)

Chapter 5 - Existence and Uniqueness of Solutions (pp. 111-140)

Chapter 6 - Iso-Differential Inequalities (pp. 141-152)

Chapter 7 - Continuous Dependence on Initial Conditions (pp. 153-162)

Chapter 8 - Existence and Uniqueness of Solutions of Systems (pp. 163-172)

Chapter 9 - General Properties of Linear Systems (pp. 173-184)

Chapter 10 - Fundamental Matrix Solution (pp. 185-192)

Chapter 11 - Periodic Linear Systems (pp. 193-200)

Chapter 12 - Asymptotic Behaviour of Solutions of Linear Systems (pp. 201-210)

Chapter 13 - Stability of Solutions (pp. 211-220)

Chapter 14 - Lyapunov’s Direct Method for Iso-Differential Systems (pp. 221-232)

Chapter 15 - Second Order Linear Iso-Differential Equations (pp. 233-246)

Chapter 16 - Green's Functions (pp. 247-254)

References

Index

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