版本 
1st ed 
說明 
xii, 344 p. : ill. ; 25 cm 
系列 
NorthHolland mathematics studies,
03040208 ; 207

附註 
Electronic reproduction. Amsterdam : Elsevier Science & Technology, 2007. Mode of access: World Wide Web. System requirements: Web browser. Title from title screen (viewed on July 25, 2007). Access may be restricted to users at subscribing institutions 

The book is an almost selfcontained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multifunction) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multifunction) to have at least one solution. The invariance of a set K with respect to a function (or multifunction) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumos Viability Theorem for ordinary differential equations with continuous righthand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multivalued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their wellknown classical counterparts.  New concepts for multifunctions as the classical tangent vectors for functions  Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions  Clarifying examples, illustrations and numerous problems, completely and carefully solved  Illustrates the applications from theory into practice  Very clear and elegant style 

Preface  Chapter 1. Generalities  Chapter 2. Specific preliminary results  Ordinary differential equations and inclusions  Chapter 3. Nagumo type viability theorems  Chapter 4. Problems of invariance  Chapter 5. Viability under Caraťhodory conditions  Chapter 6. Viability for differential inclusions  Chapter 7. Applications  Part 2 Evolution equations and inclusions  Chapter 8. Viability for singlevalued semilinear evolutions  Chapter 9. Viability for multivalued semilinear evolutions  Chapter 10. Viability for singlevalued fully nonlinear evolutions  Chapter 11. Viability for multivalued fully nonlinear evolutions  Chapter 12. Caraťhodory perturbations of mdissipative operators  Chapter 13. Applications  Solutions to the proposed problems  Bibliographical notes and comments  Bibliography  Name Index  Subject Index  Notation 

Includes bibliographical references (p. 325333) and indexes 
鏈接 
Original 9780444527615
0444527613
(OCoLC)85690133

主題 
Differential equations


Set theory


Symmetry (Mathematics)


Electronic books. local

Alt Author 
Necula, Mihai


Vrabie, I. I. (Ioan I.), 1951


ScienceDirect (Online service)

