Geodesic
The functional differential inclusions with impulses and with the right-hand side not necessarily convex-valued with respect to switching
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 43 (2014) no. 1, pp. 3-48

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The Cauchy problem for the functional differential inclusion with Volterra's multivalued map not necessarily convex-valued with respect to switching and with impulses is considered. For this problem, the definition of a generalized solution is introduced, and the questions of existence and extendibility of generalized solutions are studied. Notions of a near-realization and realization of the distance to an arbitrary summable function by the set of generalized solutions are formulated. For a set of generalized solutions of functional differential inclusions with impulses and with multivalued map not necessarily convex-valued with respect to switching, estimations are found similar to A. F. Filippov's estimations. The generalized principle of density is proved.
Keywords: functional differential inclusion, convex-valued with respect to switching, generalized solution, the near-realization and realization of the distance to a given summable function by the set of generalized solutions, a-priori boundedness. 
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     author = {A. I. Bulgakov and O. V. Filippova},
     title = {The functional differential inclusions with impulses and with the right-hand side not necessarily convex-valued with respect to switching},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {3--48},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2014_43_1_a0/}
}
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A. I. Bulgakov; O. V. Filippova. The functional differential inclusions with impulses and with the right-hand side not necessarily convex-valued with respect to switching. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 43 (2014) no. 1, pp. 3-48. http://geodesic.mathdoc.fr/item/IIMI_2014_43_1_a0/