Functional Differential Equations: Application of i-smooth calculus
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1999
|
| Series: | Mathematics and Its Applications
479 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Beginning with the works of N.N.Krasovskii [81, 82, 83], which clarified the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the same completeness as the corresponding field of ODE (ordinary differential equations) theory. The term functional differential equations (FDE) is used as a synonym for systems with delays 1. The systematic presentation of these results and further references can be found in a number of excellent books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102, 128]. In this monograph we present basic facts of i-smooth calculus ~ a new differential calculus of nonlinear functionals, based on the notion of the invariant derivative, and some of its applications to the qualitative theory of functional differential equations. Utilization of the new calculus is the main distinction of this book from other books devoted to FDE theory. Two other distinguishing features of the volume are the following: - the central concept that we use is the separation of finite dimensional and infinite dimensional components in the structures of FDE and functionals; - we use the conditional representation of functional differential equations, which is convenient for application of methods and constructions of i~smooth calculus to FDE theory |
| Physical Description: | 1 Online-Ressource (XV, 168 p) |
| ISBN: | 9789401716307 9789048152117 |
| DOI: | 10.1007/978-94-017-1630-7 |
Staff View
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| spelling | Kim, A. V. Verfasser aut Functional Differential Equations Application of i-smooth calculus by A. V. Kim Dordrecht Springer Netherlands 1999 1 Online-Ressource (XV, 168 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 479 Beginning with the works of N.N.Krasovskii [81, 82, 83], which clarified the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the same completeness as the corresponding field of ODE (ordinary differential equations) theory. The term functional differential equations (FDE) is used as a synonym for systems with delays 1. The systematic presentation of these results and further references can be found in a number of excellent books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102, 128]. In this monograph we present basic facts of i-smooth calculus ~ a new differential calculus of nonlinear functionals, based on the notion of the invariant derivative, and some of its applications to the qualitative theory of functional differential equations. Utilization of the new calculus is the main distinction of this book from other books devoted to FDE theory. Two other distinguishing features of the volume are the following: - the central concept that we use is the separation of finite dimensional and infinite dimensional components in the structures of FDE and functionals; - we use the conditional representation of functional differential equations, which is convenient for application of methods and constructions of i~smooth calculus to FDE theory Mathematics Functional analysis Differential Equations Differential equations, partial Systems theory Mathematical optimization Ordinary Differential Equations Functional Analysis Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematik Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf Funktional-Differentialgleichung (DE-588)4155668-9 s 1\p DE-604 Mathematics and Its Applications 479 (DE-604)BV008163334 479 https://doi.org/10.1007/978-94-017-1630-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kim, A. V. Functional Differential Equations Application of i-smooth calculus Mathematics and Its Applications Mathematics Functional analysis Differential Equations Differential equations, partial Systems theory Mathematical optimization Ordinary Differential Equations Functional Analysis Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematik Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| subject_GND | (DE-588)4155668-9 |
| title | Functional Differential Equations Application of i-smooth calculus |
| title_auth | Functional Differential Equations Application of i-smooth calculus |
| title_exact_search | Functional Differential Equations Application of i-smooth calculus |
| title_full | Functional Differential Equations Application of i-smooth calculus by A. V. Kim |
| title_fullStr | Functional Differential Equations Application of i-smooth calculus by A. V. Kim |
| title_full_unstemmed | Functional Differential Equations Application of i-smooth calculus by A. V. Kim |
| title_short | Functional Differential Equations |
| title_sort | functional differential equations application of i smooth calculus |
| title_sub | Application of i-smooth calculus |
| topic | Mathematics Functional analysis Differential Equations Differential equations, partial Systems theory Mathematical optimization Ordinary Differential Equations Functional Analysis Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematik Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| topic_facet | Mathematics Functional analysis Differential Equations Differential equations, partial Systems theory Mathematical optimization Ordinary Differential Equations Functional Analysis Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematik Funktional-Differentialgleichung |
| url | https://doi.org/10.1007/978-94-017-1630-7 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT kimav functionaldifferentialequationsapplicationofismoothcalculus |