Nonoscillation Theory of Functional Differential Equations with Applications - Agarwal, Ravi P.; Berezansky, Leonid; Braverman, Elena; Domoshnitsky, Alexander; SpringerLink (Online service) (New York, NY : Springer New York : Imprint: Springer, 2012)
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.      .
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.
Keywords: Partial differential equations; Special functions; Functional analysis; Partial Differential Equations; Special Functions; Functional Analysis