Abstract
We obtain measurable viability results for the differential inclusion via the approximation of F through the Aumann integral means. The admissibility of a preorder is also studied by reducing it to the viability of its sections
References
- J. P. Aubin: Viability Theory, Birkhäuser, Basel, 1991.Google Scholar
- J. P. Aubin, A. Cellina: Differential Inclusions, Springer-Verlag, Berlin et al., 1984.https://doi.org/10.1007/978-3-642-69512-4Google Scholar
- D. Bothe: Multivalued differential equations on graphs, Nonlinear Anal. 18 (1992) 245–252.https://doi.org/10.1016/0362-546X(92)90062-JGoogle Scholar
- H. Brezis, F. Browder: A general principle on ordered sets in nonlinear functional analysis, Advances in Math. 21 (1976) 355–364.https://doi.org/10.1016/S0001-8708(76)80004-7Google Scholar
- O. Cârjă, C. Ursescu: The characteristics method for a first order partial differential equation, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 39 (1993) 367–396.Google Scholar
- C. Castaing, M. Moussaoui, A. Syam: Multivalued differential equations on closed convex sets in Banach spaces, Set-Valued Anal. 1 (1994) 329–353.https://doi.org/10.1007/BF01027824Google Scholar
- C. Castaing, M. Valadier: Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin et al., 1977.https://doi.org/10.1007/BFb0087685Google Scholar
- K. Deimling: Multivalued Differential Equations, De Gruyter, Berlin, 1992.https://doi.org/10.1515/9783110874228Google Scholar
- H. Frankowska, S. Plaskacz: A measurable upper semicontinuous viability theorem for tubes, Nonlinear Anal. 26 (1996) 565–582.https://doi.org/10.1016/0362-546X(94)00299-WGoogle Scholar
- H. Frankowska, S. Plaskacz, T. Rzezuchowski: Measurable viability theorems and the Hamilton-Jacobi-Bellman equation, J. Differential Equations 116 (1995) 265–305.https://doi.org/10.1006/jdeq.1995.1036Google Scholar
- H. G. Guseinov, A. I. Subbotin, V. N. Ushakov: Derivatives for multivalued mappings with applications to game-theoretical problems of control, Problems of Control and Information Theory 14 (1985) 155–168.Google Scholar
- G. Haddad: Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math. 39 (1981) 83–100.https://doi.org/10.1007/BF02762855Google Scholar
- L. Malaguti: Monotone trajectories of differential inclusions in Banach spaces, J. Convex Anal. 3 (1996) 269–281.https://doi.org/10.68381/jca03018Google Scholar
- P. Tallos: Viability problems for non autonomous differential inclusions, SIAM J. Control Optim. 29 (1991) 253–263.https://doi.org/10.1137/0329014Google Scholar
- C. Ursescu: Carathéodory solutions of ordinary differential equations on locally closed sets in finite dimensional spaces, Math. Japon. 31 (1986) 483–491.Google Scholar
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Published by Heldermann Verlag, 2000. Rights now held by Banach Press.
