Geodesic
An existence result for impulsive functional differential inclusions in Banach spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 24 (2004) no. 1, pp. 13-30.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: impulsive functional differential inclusion, semilinear differential inclusion, mild solution, Cauchy problem, solution set, condensing multimap, fixed point 
@article{DMDICO_2004_24_1_a1,
     author = {Benedetti, Irene},
     title = {An existence result for impulsive functional differential inclusions in {Banach} spaces},
     journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
     pages = {13--30},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2004},
     zbl = {1071.34087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMDICO_2004_24_1_a1/}
}
TY  - JOUR
AU  - Benedetti, Irene
TI  - An existence result for impulsive functional differential inclusions in Banach spaces
JO  - Discussiones Mathematicae. Differential Inclusions, Control and Optimization
PY  - 2004
SP  - 13
EP  - 30
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMDICO_2004_24_1_a1/
LA  - en
ID  - DMDICO_2004_24_1_a1
ER  - 
%0 Journal Article
%A Benedetti, Irene
%T An existence result for impulsive functional differential inclusions in Banach spaces
%J Discussiones Mathematicae. Differential Inclusions, Control and Optimization
%D 2004
%P 13-30
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMDICO_2004_24_1_a1/
%G en
%F DMDICO_2004_24_1_a1
Benedetti, Irene. An existence result for impulsive functional differential inclusions in Banach spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 24 (2004) no. 1, pp. 13-30. http://geodesic.mathdoc.fr/item/DMDICO_2004_24_1_a1/

[1] N.U. Ahmed, Systems governed by impulsive differential inclusions on Hilbert spaces, Nonlinear Anal, 45 (6) (2001), Ser. A: Theory Methods, 693-706.

[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] 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.

[4] M. Benchohra, J. Henderson and S.K. Ntouyas, On first order impulsive differential inclusions with periodic boundary conditions, Advances in impulsive differential equations. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 9 (3) (2002), 417-427.

[5] M. Benchohra and S.K. Ntouyas, Existence results for multivalued semilinear functional-differential equations, Extracta Math. 18 (1) (2003), 1-12.

[6] K. Deimling, Multivalued differential equations, de Gruyter Series in Nonlinear Analysis and Applications, 1, Walter de Gruyter, Berlin 1992.

[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.

[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] 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.

[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] 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.

[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.

[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.

[14] G.V. Smirnov, Introduction to the theory of differential inclusions, Graduate Studies in Mathematics, 41, American Mathematical Society, Providence, RI 2002.

[15] A.A. Tolstonogov, Differential inclusions in a Banach space, Mathematics and its Applications, 524, Kluwer Academic Publishers, Dordrecht 2000.

[16] P.J. Watson, Impulsive differential inclusions, Nonlinear World 4 (4) (1997), 395-402.