ON THE SOLUTION SETS OF DIFFERENTIAL INCLUSION IN BANACH SPACES

Authors

  • A. ANGURAJ Department of Mathematics, Bharathiar University, Coimbato-re 641 046, Tamil Nadu India.
  • K. BALACHANDRAN Department of Mathematics, Bharathiar University, Coimbato-re 641 046, Tamil Nadu India.

DOI:

https://doi.org/10.5556/j.tkjm.23.1992.4527

Keywords:

classical solutions, differential inclusion in a Banach space, retract

Abstract

We prove the set of all classical solutions of the differential inclusion

\[ \dot x(t) \in A(t,x) +F(t,x,\dot x) \quad x(t_0) = x_0, \dot x(t_0) = y_0 \]

is a retract of the space $C^1$.

References

T. P. Aubin and A. Cellina, "Differential Inclusions", Springer-Verlag (1984).

L. Gorniewicz, "On the solution sets of differential inclusions", J. Math. Anal. Appl., 113 (198-6) 235-244.

C. Himmelberg and F. Van Vleck "A note on the solution sets of differential inclusions", Rocky Mountain J. Math., 12 .(1982) 621-625.

E. Michael, "Continuous selections I", Ann. of Math., 63 (1956) 361-382.

N. S. Papageorgiou, "On multivalued evolution equations and differential inclusions in Banach spaces"., Comment. Math. Univ. Sancli Pauli, 36 (1987), 21-39.

B. Ricceri, "Une propTiete topologigue·de l'ensemble des pomts fixes d'une contract10n multivoque a -valeures convexes", Atti Aceacl. Naz.. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 81 {1987) 28-3-286.

O. N. Ricceri, Classical solutions of the problem x'in F(t,x,x'), x(t_0) = x_0, x'(t_0) = y_0 in Banach spaces, Funkcial. Ekvac. 3,1 (1991) 127-141.

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Published

1992-03-01

How to Cite

ANGURAJ, A., & BALACHANDRAN, K. (1992). ON THE SOLUTION SETS OF DIFFERENTIAL INCLUSION IN BANACH SPACES. Tamkang Journal of Mathematics, 23(1), 59-65. https://doi.org/10.5556/j.tkjm.23.1992.4527

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Papers