Nonoscillation Theory of Functional Differential Equations with Applications

ISBN-13: 9781461434542 / Angielski / Twarda / 2012 / 520 str.

Ravi P. Agarwal; Leonid Berezansky; Elena Braverman

Opis

This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.​

Recenzje

From the reviews:

"We strongly recommend the monograph for applied mathematicians, researchers in different field of engineering and graduate students planning their further study in the field of functional differential equations. ... The book is well organized, easy to read; senior undergraduate students will be able to follow the proofs and explanations. The monograph could be one of the basic handbooks consulted for studying and understanding functional differential equations and their oscillation theory." (Haydar Akca, Zentralblatt MATH, Vol. 1253, 2013)

"The book under review complements the theory of delay equations by mainly focusing on nonoscillation, and its relation with stability, boundary value problems, and some other close subjects. It is completely self-contained. ... This book is a useful and good reference for researchers in qualitative theory of ordinary differential equations ... . It can also be useful as a textbook or to initiate research in the subject." (Basak Karpuz, Mathematical Reviews, January, 2013)

Spis treści

1. Introduction to Oscillation Theory.- 2. Scalar Delay Differential Equations on Semiaxes.- 3. Scalar Delay Differential Equations on Semiaxis with Positive and Negative Coefficients.- 4. Oscillation of Equations with a Distributed Delay.- 5. Scalar Advanced and Mixed Differential Equations on Semiaxes.- 6. Neutral Differential Equations.- 7. Second Order Delay Differential Equations.- 8. Second Order Delay Differential Equations with Damping Terms.- 9. Vector Delay Differential Equations.- 10. Linearized Methods for Nonlinear Equations with a Distributed Delay.- 11. Nonlinear Models - Modifications of Delay Logistic Equations.- 12. First Order Linear Delay Impulsive Differential Equation.- 13. Second Order Linear Delay Impulsive Differential Equations.- 14. Linearized Oscillation Theory for Nonlinear Delay Impulsive Equations.- 15. Maximum Principles and Nonoscillation Intervals for First Order Volterra Functional Differential Equations.- 16. Systems of Functional Differential Equations on Finite Intervals.- 17. Nonoscillation Interval for n-th Order Functional Differential Equations.- Appendix A.- Appendix B. ​