Geodesic
On some boundary-value problems for functional-differential inclusions in Banach spaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 36-44.

Voir la notice de l'article provenant de la source Math-Net.Ru

The general boundary-value problem for a semilinear functional-differential inclusion in a separable Banach space is considered. A many-valued integral operator whose fixed points are integral solutions to the problem is constructed. Conditions ensuring this many-valued operator to be condensing with respect to the vector measure of noncompactness are investigated. Application of topological degree theory allows one to establish some existence theorems for the boundary-value problem. The Cauchy problem and the periodic problem are considered as special cases. 
@article{CMFD_2006_15_a3,
     author = {M. M. Basova and V. V. Obukhovskii},
     title = {On some boundary-value problems for functional-differential inclusions in {Banach} spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {36--44},
     publisher = {mathdoc},
     volume = {15},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_15_a3/}
}
TY  - JOUR
AU  - M. M. Basova
AU  - V. V. Obukhovskii
TI  - On some boundary-value problems for functional-differential inclusions in Banach spaces
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2006
SP  - 36
EP  - 44
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2006_15_a3/
LA  - ru
ID  - CMFD_2006_15_a3
ER  - 
%0 Journal Article
%A M. M. Basova
%A V. V. Obukhovskii
%T On some boundary-value problems for functional-differential inclusions in Banach spaces
%J Contemporary Mathematics. Fundamental Directions
%D 2006
%P 36-44
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2006_15_a3/
%G ru
%F CMFD_2006_15_a3
M. M. Basova; V. V. Obukhovskii. On some boundary-value problems for functional-differential inclusions in Banach spaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 36-44. http://geodesic.mathdoc.fr/item/CMFD_2006_15_a3/

[1] Ding Z., Kartsatos A. G., “Nonresonance problems for differential inclusions in separable Banach spaces”, Proc. Amer. Math. Soc., 124:8 (1996), 2357–2365 | DOI | MR | Zbl

[2] Kamenskii M., Obukhovskii V., “Condensing multioperators and periodic solutions of parabolic functional-differential inclusions in Banach spaces”, Nonlinear Anal., 20:7 (1993), 781–792 | DOI | MR

[3] Kamenskii M., Obukhovskii V., Zecca P., Condensing multivalued maps and semilinear differential inclusions in Banach spaces, Walter de Gruyter, Berlin, New York, 2001 | MR

[4] Kravvaritis D., Papageorgiou N. S., “A boundary value problem for a class of evolution inclusions”, Comment. Math. Univ. St. Paul., 40:1 (1991), 29–37 | MR | Zbl

[5] Marino G., “Nonlinear boundary value problems for multivalued differential equations in Banach spaces”, Nonlinear Anal., 14:7 (1990), 545–558 | DOI | MR | Zbl

[6] Obukhovskii V., Zecca P., “On boundary value problems for degenerate differential inclusions in Banach spaces”, Abstr. Appl. Anal., 2003, no. 13, 769–784 | DOI | MR | Zbl

[7] Papageorgiou N. S., “Boundary value problems for evolution inclusions”, Comment. Math. Univ. Carolin., 29:2 (1988), 355–363 | MR | Zbl

[8] Papageorgiou N. S., “Boundary value problems and periodic solutions for semilinear evolution inclusions”, Comment. Math. Univ. Carolin., 35:2 (1994), 325–336 | MR | Zbl

[9] Zecca P., Zezza P. L., “Nonlinear boundary value problems in Banach spaces for multivalue differential equations on a noncompact interval”, Nonlinear Anal., 3:3 (1979), 347–352 | DOI | MR | Zbl