Two existence results for monotone trajectories of differential inclusions x' (t) ∈ F (t, x(t)) in a separable Banach space are obtained; they extend in two directions previous ones due to Aubin-Cellina, Deimling and Haddad.

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Luisa Malaguti

Dipartimento di Matematica Pura e Applicata, Università di Modena, via Campi 213/B, 41100 Modena, Italy

  1. J.P. Aubin, A. Cellina: Differential Inclusions, Springer-Verlag, Berlin, 1984.https://doi.org/10.1007/978-3-642-69512-4Google Scholar
  2. H. Benabdellah, C. Castaing and M.A. Gamal Ibrahim: BV solutions of multivalued differential equations on closed moving sets in Banach spaces, Sém. d’Anal. Convexe Montpellier, Exposé 10, 1992.Google Scholar
  3. D. Bothe: Multivalued differential equations on graphs, Nonlinear Anal. 18 (1992) 245–252.https://doi.org/10.1016/0362-546X(92)90062-JGoogle Scholar
  4. C. Castaing, M.D.P. Monteiro Marques: Sweeping processes by nonconvex closed moving sets with perturbation, C.R. Acad. Sci. Paris, t. 319, Série I (1994) 127-132.Google Scholar
  5. C. Castaing, M. Moussaoui and A. Syam: Multivalued differential equations on closed moving sets in Banach spaces, Set-Valued Analysis 1 (1994) 329–353.https://doi.org/10.1007/BF01027824Google Scholar
  6. C. Castaing, M. Valadier: Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer Verlag, Berlin, 1977.https://doi.org/10.1007/BFb0087685Google Scholar
  7. F. H. Clarke: Optimization and Nonsmooth Analysis, Wiley-Interscience, 1983.Google Scholar
  8. K. Deimling: Multivalued differential equations on closed sets, Differential and Integral Equations 1 (1988) 23–30.https://doi.org/10.57262/die/1371747579Google Scholar
  9. 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
  10. P. Tallos: Viability problems for nonautonomous differential inclusions, Siam J. Control Optim. 29 (1991) 253–263.https://doi.org/10.1137/0329014Google Scholar

L. Malaguti. “Monotone Trajectories of Differential Inclusions in Banach Spaces.” Journal of Convex Analysis 3 (1996), No. 2, 269–281. https://doi.org/10.68381/jca03018