Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Delay differential inclusions with constraints


Authors: Shou Chuan Hu and Nikolaos S. Papageorgiou
Journal: Proc. Amer. Math. Soc. 123 (1995), 2141-2150
MSC: Primary 34K15; Secondary 34A60, 49J24
DOI: https://doi.org/10.1090/S0002-9939-1995-1257111-9
MathSciNet review: 1257111
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we examine functional differential inclusions with memory and state constraints. For the case of time-independent state constraints, we show that the solution set is $ {R_\delta }$ under Carathéodory conditions on the orientor field. For the case of time-dependent state constraints we prove two existence theorems. For this second case, the question of whether the solution set is $ {R_\delta }$ remains open.


References [Enhancements On Off] (What's this?)

  • [1] N. Aronszajn, Le corespondant topologique de l'unicité dans la theorie des equations differentielles, Ann. of Math. 43 (1942), 730-738. MR 0007195 (4:100e)
  • [2] J.-P. Aubin and A. Cellina, Differential inclusions, Springer-Verlag, Berlin, 1984. MR 755330 (85j:49010)
  • [3] F. S. DeBlasi and J. Myjak, On the solution set for differential inclusions, Bull. Polish Acad. Sci. 33 (1985), 17-23.
  • [4] S. Eilenberg and D. Montgomery, Fixed point theorems for multivalued transformations, Amer. J. Math. 68 (1946), 214-222. MR 0016676 (8:51a)
  • [5] E. Flytzanis and N. S. Papageorgiou, Existence of monotone and slow solutions for differential inclusions, Internat. J. Systems Sci. 20 (1989), 2241-2249. MR 1031152 (90j:34024)
  • [6] G. Haddad, Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math. 39 (1981), 83-100. MR 617292 (83b:34019)
  • [7] G. Haddad and J.-M. Lasry, Periodic solutions of functional differential inclusions and fixed points of $ \sigma $-selectionable correspondences, J. Math. Anal. Appl. 96 (1983), 295-312. MR 719317 (84m:34015)
  • [8] C. J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 59-71. MR 0367142 (51:3384)
  • [9] C. J. Himmelberg and F. S. Van Vleck, On the topological triviality of the solution sets, Rocky Mountain J. Math. 10 (1980), 247-252. MR 573874 (81g:34006)
  • [10] -, A note on the solution sets of differential inclusions, Rocky Mountain J. Math. 12 (1982), 621-625. MR 683856 (84b:34019)
  • [11] S. Hu and N. S. Papageorgiou, On the topological regularity of the solution set of differential inclusions with constraints, J. Differential Equations 107 (1994), 280-289. MR 1264523 (94m:34036)
  • [12] D. Hyman, On decreasing sequences of compact absolute retracts, Fund. Math. 64 (1969), 91-97. MR 0253303 (40:6518)
  • [13] M. Kisielewicz, Z. Nowak, and M. Przybybowska, An approximation theorem for vector valued functions, Funct. Approx. Comment. Math. XII (1982), 55-62. MR 817307 (86m:41039)
  • [14] N. S. Papageorgiou, On measurable multifunctions with applications to random multivalued equations, Math. Japon. 32 (1987), 437-464. MR 914749 (89a:54019)
  • [15] L. Rybinski, On Carathéodory type selections, Fund. Math. 125 (1985), 187-193. MR 813756 (87k:28012)
  • [16] J. Yorke, Spaces of solutions, Lecture Notes in Oper. Res. and Math., vol. 12, Springer-Verlag, Berlin, 1969, pp. 383-403. MR 0361294 (50:13739)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34K15, 34A60, 49J24

Retrieve articles in all journals with MSC: 34K15, 34A60, 49J24


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1257111-9
Keywords: Upper semicontinuous multifunction, $ {R_\delta }$-set, tangent cone, periodic solution, Hausdorff metric, time-varying constraint
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society