Nagumo viability theorem. Revisited

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 9, 2006, Pages 2043-2052

  Vrabie, Ioan I ^a  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

b compact function; Lipschitz function; Pseudoparabolic equation; Slow fluids; Tangency condition; Viable set

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; NONLINEAR EQUATIONS;

B-COMPACT FUNCTION; LIPSCHITZ FUNCTION; PSEUDOPARABOLIC EQUATION; SLOW FLUIDS; TANGENCY CONDITION; VIABLE SET;

THEOREM PROVING;

EID: 33344477153     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.07.037     Document Type: Article

References (13)

1. S.N. Antontsev, J.I. Díaz, S.I. Shmarev, Energy methods for free boundary problems: Applications to nonlinear PDSs and fluid mechanics, Progress in Nonlinear Differential Equations and Their Applications, vol. 48, Birkhäuser, Basel, Boston, Berlin, 2002.
2. H. Brezis On a characterization of flow-invariant sets Comm. Pure Appl. Math. 23 1970 261 263
3. O. Cârjǎ, I.I. Vrabie, Differential equations on closed sets, in: A. Cañada, P. Drabek, A. Fonda (Eds.), Handbook of Differential Equations, vol. 2, Ordinary Differential Equations, 2005, pp. 147-238.
4. M.G. Crandall A generalization of Peano's existence theorem and flow-invariance Proc. Am. Math. Soc. 36 1972 151 155
5. J.I. Díaz, and R. Quintanilla Spatial and continuous dependence estimates in linear viscoelasticity J. Math. Anal. Appl. 273 2002 1 16
6. M. Frigon, and D. O'Reagan Existence results for initial value problems in Banach spaces Differential Equations Dynamical Syst. 2 1994 41 48
7. P. Hartman On invariant sets and on a theorem of Ważewski Proc. Am. Math. Soc. 32 1972 511 520
8. M. Nagumo Über die Lage der Integralkurven gewönlicher Differentialgleichungen Proc. Phys. Math. Soc. Jpn. 24 1942 551 559
9. I.I. Vrabie, Compactness methods for nonlinear evolutions, second ed., Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 75, Longman, 1995.
10. 0-semigroups and applications, North-Holland Mathematics Studies, vol. 191, Elsevier, Amsterdam, 2003.
11. I.I. Vrabie Differential Equations. An Introduction to Basic Concepts, Results and Applications 2004 World Scientific Singapore
12. J.A. Yorke Invariance for ordinary differential equations Math. Syst. Theory 1 1967 353 372
13. J.A. Yorke Invariance for ordinary differential equations: correction Math. Syst. Theory 2 1968 381