Viable Solutions for a Class of Delay Evolution Problems
Abstract
In this paper, we give existence results for viable solutions in the so-called fully constrained set for functional differential inclusions in Banach spaces for a non-autonomous set-valued mapping with convex compact values. We study also the time dependent case of these invariance sets.References
J.P. Aubin, Viability theory, Springer-Verlag, Boston, 1991.
H. Benabdellah and A. Faik, Perturbations convexes et nonconvexes des équations d'evolution, Portugal. Math, 53(2)(1996), 187-208.
H. Benabdelah, C. Castaing and M.A. G. Ibrahim, BV solutions of multivalued differential equations on closed moving sets in Banach spaces, Geometry in Nonlinear Control and Differential Inclusions, V.32(1995), 53-81.
C. Castaing, M.A.G. Ibrahim and M.F. Yarou , Some contributions to nonconvex sweeping process, Journal of Nonlinear and Convex Analysis, vol. 10, no. 1, (2009) 1-20
C. Castaing, M.A.G. Ibrahim and M.F. Yarou , Existence problems in second order evolution inclusions: discretization and variational approach, Taiwanese Journal of Mathematics, Vol. 12, No. 6, (2008) 1433-1475.
C. Castaing and M.D.P. Monteiro Marques, A Multivalued version of Scorza- Dragoni's theorem with an application to normal integrands , Bull. Pol. Acad. Sci. Mathematics, 42 (1994) 133-140.
C. Castaing, M. Moussaoui and A. Syam, Multivalued differential equations on closed convex sets in Banach spaces, Set-Valued Analysis,1 (1994), 329-353.
C. Castaing, M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math. 580, Springer-Verlag, Berlin 1977.
K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin, New York, 1992.
G. Haddad, Monotone viable trajectories for functional differential inclusions, J. Differ. Equations, 42 (1981), 1-24.
W. Jachimiak, Viability for functional differential equations, Bulletin of the Polish Academy of Sciences Mathematics, V.42, n.1, (1994) 55-61.
E. Mitidier and I.I. Vrabie, Existence for nonlinear functional differential equations, Hiroshima Math. J., 17 (1987), 627-649.
A. Syam, Contribution aux inclusions differentielles, These. Universite de Montpellier II,1993.
M.F. Yarou, Discretisation methods for nonconvex differential inclusions, EJQTDE, 12, (2009), 1-10.2009.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).