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| 001 | ocn162131435 | ||
| 003 | OCoLC | ||
| 005 | 20141103172228.0 | ||
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| 008 | 070802s2007 ne a ob 001 0 eng d | ||
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| 019 |
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| 020 | _a9780444527615 | ||
| 020 | _a0444527613 | ||
| 020 | _a9780080521664 (electronic bk.) | ||
| 020 | _a0080521665 (electronic bk.) | ||
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_a(OCoLC)162131435 _z(OCoLC)170967912 _z(OCoLC)441781564 _z(OCoLC)648244998 _z(OCoLC)779920595 |
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| 037 |
_a133439:133563 _bElsevier Science & Technology _nhttp://www.sciencedirect.com |
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| 050 | 4 |
_aQA371 _b.C37 2007 |
|
| 072 | 7 |
_aMAT _x007000 _2bisacsh |
|
| 082 | 0 | 4 |
_a515.35 _222 |
| 049 | _aTEFA | ||
| 100 | 1 | _aC�arj�a, Ovidiu. | |
| 245 | 1 | 0 |
_aViability, invariance and applications _h[electronic resource] / _cOvidiu C�arj�a, Mihai Necula, Ioan I. Vrabie. |
| 250 | _a1st ed. | ||
| 260 |
_aAmsterdam ; _aBoston : _bElsevier, _c2007. |
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| 300 |
_a1 online resource (xii, 344 p.) : _bill. |
||
| 490 | 1 |
_aNorth-Holland mathematics studies, _x0304-0208 ; _v207 |
|
| 520 | _aThe book is an almost self-contained 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 multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) 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 right-hand 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. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. - New concepts for multi-functions 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. | ||
| 505 | 0 | _aPreface -- 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 Carat�hodory conditions -- Chapter 6. Viability for differential inclusions -- Chapter 7. Applications -- Part 2 Evolution equations and inclusions -- Chapter 8. Viability for single-valued semilinear evolutions -- Chapter 9. Viability for multi-valued semilinear evolutions -- Chapter 10. Viability for single-valued fully nonlinear evolutions -- Chapter 11. Viability for multi-valued fully nonlinear evolutions -- Chapter 12. Carat�hodory perturbations of m-dissipative operators -- Chapter 13. Applications -- Solutions to the proposed problems -- Bibliographical notes and comments -- Bibliography -- Name Index -- Subject Index -- Notation. | |
| 504 | _aIncludes bibliographical references (p. 325-333) and indexes. | ||
| 588 | _aDescription based on print version record. | ||
| 650 | 0 | _aDifferential equations. | |
| 650 | 0 | _aSet theory. | |
| 650 | 0 | _aSymmetry (Mathematics) | |
| 650 | 7 |
_aMATHEMATICS _xDifferential Equations _xGeneral. _2bisacsh |
|
| 650 | 7 |
_aDifferential equations. _2fast _0(OCoLC)fst00893446 |
|
| 650 | 7 |
_aSet theory. _2fast _0(OCoLC)fst01113587 |
|
| 650 | 7 |
_aSymmetry (Mathematics) _2fast _0(OCoLC)fst01739417 |
|
| 655 | 4 | _aElectronic books. | |
| 700 | 1 | _aNecula, Mihai. | |
| 700 | 1 |
_aVrabie, I. I. _q(Ioan I.), _d1951- |
|
| 776 | 0 | 8 |
_iPrint version: _aC�arj�a, Ovidiu. _tViability, invariance and applications. _b1st ed. _dAmsterdam ; Boston : Elsevier, 2007 _z9780444527615 _z0444527613 _w(OCoLC)85690133 |
| 830 | 0 |
_aNorth-Holland mathematics studies ; _v207. _x0304-0208 |
|
| 856 | 4 | 0 |
_3ScienceDirect _uhttp://www.sciencedirect.com/science/book/9780444527615 |
| 856 | 4 |
_uhttp://www.sciencedirect.com/science/publication?issn=03040208&volume=207 _3Volltext |
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| 938 |
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| 938 |
_aIngram Digital eBook Collection _bIDEB _n102155 |
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| 938 |
_aEBSCOhost _bEBSC _n196523 |
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| 942 | _cEB | ||
| 994 |
_aC0 _bTEF |
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| 999 |
_c21984 _d21984 |
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