TY  - BOOK
AU  - Lakshmikantham,V.
AU  - Leela,S.
AU  - Drici,Zahia
AU  - McRae,F.A.
ED  - SpringerLink (Online service)
TI  - Theory of Causal Differential Equations
T2  - Atlantis Studies in Mathematics for Engineering and Science,
SN  - 9789491216251
AV  - QA372 
U1  - 515.352 23
PY  - 2010///
CY  - Paris
PB  - Atlantis Press
KW  - Mathematics
KW  - Differential Equations
KW  - Differential equations, partial
KW  - Ordinary Differential Equations
KW  - Partial Differential Equations
N1  - Preliminaries -- Basic Theory -- Theoretical ApproximationMethods -- Stability Theory -- Miscellaneous Topics in Causal Systems
N2  - The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.2991/978-94-91216-25-1
ER  -