THEORY OF CAUSAL DIFFERENTIAL EQUATIONS

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Leela, S. (Autor), Lakshmikantham, V. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Paris : Atlantis Press : Imprint: Atlantis Press, 2010.
Edición:1st ed. 2010.
Colección:Atlantis Studies in Mathematics for Engineering and Science, 5
Temas:
Differential equations.
Differential Equations.
Acceso en línea:Texto Completo

MARC

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100 1 |a Leela, S.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a THEORY OF CAUSAL DIFFERENTIAL EQUATIONS  |h [electronic resource] /  |c by S. Leela, V. Lakshmikantham. 
250 |a 1st ed. 2010. 
264 1 |a Paris :  |b Atlantis Press :  |b Imprint: Atlantis Press,  |c 2010. 
300 |a XI, 208 p.  |b online resource. 
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490 1 |a Atlantis Studies in Mathematics for Engineering and Science,  |x 2467-9631 ;  |v 5 
505 0 |a Preliminaries -- Basic Theory -- Theoretical ApproximationMethods -- Stability Theory -- Miscellaneous Topics in Causal Systems. 
520 |a 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. 
650 0 |a Differential equations. 
650 1 4 |a Differential Equations. 
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950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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