EXISTENCE OF SOLUTIONS OF IMPLICIT DIFFERENTIAL INCLUSIONS

Authors

  • A. ANGURAJ Gobi Arts College, Gobichettipalayam-638 453, Tamil Nadu, India.
  • K. BALACHANDRAN Department of Mathematics, Bharathiar University Coimbatorc-641 046, Tamil Nadu, India.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4493

Keywords:

existence of solutions, implicit differential inclusions, Covitz-Nadler fixed point theorem

Abstract

We prove the existence of solutions for the implicit differen- tial inclusions of the form

\[ \dot x(t) \in A(t,x)+F(t,x,\dot x) \text{ for } t \in I, \text{ a.e. }  \qquad x(r) =0 \]

with $I = [r,r+a]$ by using the Covitz-Nadler fixed point theorem.

References

A. Anguraj and K. Balachandran, "On the solution sets of differential inclusion in Banach spaces", Tamkang J. Math. 23 (1992), No. 2, 57-63.

J. P. Aubin and A. Cellina, "Differential Inclusions", Springer-Verlag, Berlin, 1984.

.J. R. Bridgland, T. F., "Trajectory integrals of setvalued functions", Pacific J. Math., 33 (1970), 43-67.

A. Fryszkowski, "Continuous selections for a class of nonconvex multivalued maps", Studia Math., 76 (1983), 163-174.

M. Kisielewicz, "Subtrajectory integrals of setvalued functions and neutral functional differential inclusions", Funkcialaj Ekvacioj, 32 (1989), 163-18 9.

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

N. S. Papageorgiou, ''On the theory of functional differential inclusions of neutral type in Banach spaces", Funkcialaj Ekvacioj, 31 (1988), 103-120.

0 . N. Ricceri, "Classical solutions of the problem dot x in F(t, x, x), x(to) = xo, x(to) = Yo in Banach spaces", Funkcialaj Ekvacioj, 34 (1991), 127-141.

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Published

1993-06-01

How to Cite

ANGURAJ, A., & BALACHANDRAN, K. (1993). EXISTENCE OF SOLUTIONS OF IMPLICIT DIFFERENTIAL INCLUSIONS. Tamkang Journal of Mathematics, 24(2), 221-227. https://doi.org/10.5556/j.tkjm.24.1993.4493

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Papers