Basic Topological Structures of Ordinary Differential Equations
Traditionally, equations with discontinuities in space variables follow the ideology of the 'sliding mode'. This book contains the first account of the theory which allows the consideration of exact solutions for such equations. The difference between the two approaches is illustrated by scalar equations of the type y =f(y) and by equations arising under the synthesis of optimal control. A detailed study of topological effects related to limit passages in ordinary differential equations widens …
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- Full title :Basic Topological Structures of Ordinary Differential Equations.
Summary
Traditionally, equations with discontinuities in space variables follow the ideology of the 'sliding mode'. This book contains the first account of the theory which allows the consideration of exact solutions for such equations. The difference between the two approaches is illustrated by scalar equations of the type y =f(y) and by equations arising under the synthesis of optimal control. A detailed study of topological effects related to limit passages in ordinary differential equations widens the theory for the case ...
Read More ↓Edition Statements
- Publication Date:1998.
Publication Statements
- Publisher(s):Kluwer Academic Publishers
- Place of Publication:Dordrecht
- Language:eng
- Publication Date:1998.
The Physical Object
- Description:516 p.
Edition Identifiers
- ISBN:9780792349518, 0792349512
- oclc:ocn756473343
- Dewey Decimal:515.352
Table of Contents
1. Topological and Metric Spaces -- 2. Some Properties of Topological, Metric a Euclidean Spaces -- 3. Spaces of Mappings and Spaces of Compact Subsets -- 4. Derivation and Integration -- 5. Weak Topology on the Space L1and Derivation of Convergent Sequences -- 6. Basic Properties of Solution Spaces -- 7. Convergent Sequences of Solution Spaces -- 8. Peano, Caratheodory and Davy Conditions -- 9. Comparison Theorem -- 10. Changes of Variables, Morphisms and Maximal Extensions 11. Some Methods of Investigation of Equations -- 12. Equations and Inclusions with Complicated Discontinuities in the Space Variables -- 13. Equations and Inclusions of Second Order -- Cauchy Problem Theory -- 14. Equations and Inclusion of Second Order -- Periodic Solutions, Dirichlet Problem -- 15. Behavior of Solutions -- 16. Two-Dimensional Systems.
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