An existence result for impulsive functional differential inclusions in Banach spaces

Irene Benedetti

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2004)

  • Volume: 24, Issue: 1, page 13-30
  • ISSN: 1509-9407

Abstract

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We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.

How to cite

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Irene Benedetti. "An existence result for impulsive functional differential inclusions in Banach spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 24.1 (2004): 13-30. <http://eudml.org/doc/271453>.

@article{IreneBenedetti2004,
abstract = {We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.},
author = {Irene Benedetti},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {impulsive functional differential inclusion; semilinear differential inclusion; mild solution; Cauchy problem; solution set; condensing multimap; fixed point; impulsive functional-differential inclusions; fixed-point},
language = {eng},
number = {1},
pages = {13-30},
title = {An existence result for impulsive functional differential inclusions in Banach spaces},
url = {http://eudml.org/doc/271453},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Irene Benedetti
TI - An existence result for impulsive functional differential inclusions in Banach spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2004
VL - 24
IS - 1
SP - 13
EP - 30
AB - We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.
LA - eng
KW - impulsive functional differential inclusion; semilinear differential inclusion; mild solution; Cauchy problem; solution set; condensing multimap; fixed point; impulsive functional-differential inclusions; fixed-point
UR - http://eudml.org/doc/271453
ER -

References

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  2. [2] J.P. Aubin and A. Cellina, Differential inclusions. Set valued maps and viabilty theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] , 264, Springer-Verlag, Berlin 1984. 
  3. [3] M. Benchohra, J. Henderson, S.K. Ntouyas and A.Ouahabi, On initial value problems for a class of first order impulsive differential inclusions, Discuss. Math. Differ. Incl. Control. Optim. 21 (2) (2001), 159-171. 
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  5. [5] M. Benchohra and S.K. Ntouyas, Existence results for multivalued semilinear functional-differential equations, Extracta Math. 18 (1) (2003), 1-12. Zbl1044.34037
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  7. [7] M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, de Gruyter Series in Nonlinear Analysis and Applications, 7, Walter de Gruyter, Berlin 2001. Zbl0988.34001
  8. [8] M. Kisielewicz, Differential inclusions and optimal control, Mathematics and its Applications (East European Series), 44, Kluwer Academic Publishers Group, Dordrecht, Polish Scientific Publishers, Warsaw 1991. 
  9. [9] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6, World Scientific Publishing Co., Inc., Teaneck, NJ 1989. Zbl0719.34002
  10. [10] V.V. Obukhovskii, Semilinear functional-differential inclusions in a Banach space and controlled parabolic systems, Soviet J. Automat. Inform. Sci. 24 (1991), 71-79. 
  11. [11] R. Precup, A Granas type approach to some continuation theorems and periodic boundary value problems with impulses, Topol. Methods Nonlinear Anal. 5 (2) (1995), 385-396. Zbl0847.34028
  12. [12] A.M. Samoilenko and N.A. Perestyuk, Impulsive differential equations, World Scientific Series on Nonlinear Science, Series A: Monographs and Treatises, 14, World Scientific Publishing Co., Inc., River Edge, NJ 1995. Zbl0837.34003
  13. [13] G.Ch. Sarafova and D.D. Bainov, Periodic solutions of nonlinear integro-differential equations with an impulse effect, Period. Math. Hungar. 18 (2) (1987), 99-113. Zbl0629.34049
  14. [14] G.V. Smirnov, Introduction to the theory of differential inclusions, Graduate Studies in Mathematics, 41, American Mathematical Society, Providence, RI 2002. Zbl0992.34001
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  16. [16] P.J. Watson, Impulsive differential inclusions, Nonlinear World 4 (4) (1997), 395-402. Zbl0944.34007

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