Differential inclusions in a banach space /
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| Author / Creator: | Tolstonogov, A. A. |
|---|---|
| Uniform title: | Differentsialʹnye vkli͡uchenii͡a v banakhovom prostranstve. English |
| Imprint: | Dordrecht ; Boston, Mass. : Kluwer Academic Publishers, c2000. |
| Description: | xv, 302 p. ; 25 cm. |
| Language: | English |
| Series: | Mathematics and its applications ; v. 524 Mathematics and its applications (Kluwer Academic Publishers) ; v. 524. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4384898 |
Table of Contents:
- Preface
- 1.. Multi-Valued Differential Equation Generated by a Differential Inclusion
- 1.. Background of the theory of measurable multi-valued mappings and differential inequalities
- 2.. Existence of local solutions of a multi-valued differential equation with conditions of compactness type
- 3.. Existence of local solutions of a multi-valued differential equation. Comparison theorems
- 4.. Global solutions of a multi-valued differential equation
- 5.. Existence theorems of solutions of the multi-valued operator equation
- 6.. Notes and Remarks
- 2.. Differential Inclusions. Existence of Solutions
- 1.. Types of solutions of a differential inclusion
- 2.. Semicontinuous multi-functions
- 3.. Strongly measurable selectors of multi-functions
- 4.. Continuous selectors of multi-functions with decomposable values
- 5.. Continuous selectors of a multi-valued mappings generated by differential inclusions with non-convex right hand side
- 6.. Multi-valued selectors of a multi-valued mapping generated by a differential inclusion
- 7.. Existence of solutions of a differential inclusion with nonconvex right hand side continuous in x
- 8.. Existence of the solution of a differential inclusion with right hand side semicontinuous in x
- 9.. Notes and Remarks
- 3.. Properties of Solutions
- 1.. Auxiliary results
- 2.. The density theorems
- 3.. The co-density theorems
- 4.. Compactness of the set of solutions
- 5.. Dependence of the set of solutions on initial conditions and parameters
- 6.. Connectedness of the set of solutions
- 7.. Notes and remarks
- 4.. Integral Funnel of the Differential Inclusion
- 1.. Auxiliary lemmas
- 2.. The equation of the integral funnel
- 3.. Solutions of the equation of the integral funnel
- 4.. Properties of solutions of the equation of the integral funnel
- 5.. Properties of the integral funnel
- 6.. Extreme points of the set of solutions of a linear differential inclusion
- 7.. Notes and Remarks
- 5.. Inclusions With Non-Compact Right Hand Side
- 1.. Continuous selectors of fixed point sets of multi-functions with decomposable values
- 2.. Properties of the multi-valued Nemytskii operator
- 3.. Continuous selectors of fixed point sets of the multi-valued Nemytskii operator
- 4.. Existence and properties of solution sets of differential inclusion
- 5.. Notes and Remarks
- Appendices
- A.
- 1.. Non-convex problem of calculus of variations
- 2.. Existence of optimal control without assumptions of convexity
- 3.. Extension in continuity of multi-valued mappings
- 4.. Equivalence of differential inclusions and control systems
- References
- Index
- Symbols
