Abstract:
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.
Citation:
M. M. Basova, V. V. Obukhovskii, “On some boundary-value problems for functional-differential inclusions in Banach spaces”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, CMFD, 15, PFUR, M., 2006, 36–44; Journal of Mathematical Sciences, 149:4 (2008), 1376–1384
\Bibitem{BasObu06}
\by M.~M.~Basova, V.~V.~Obukhovskii
\paper On some boundary-value problems for functional-differential inclusions in Banach spaces
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~1
\serial CMFD
\yr 2006
\vol 15
\pages 36--44
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd38}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336427}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 4
\pages 1376--1384
\crossref{https://doi.org/10.1007/s10958-008-0071-7}
Linking options:
https://www.mathnet.ru/eng/cmfd38
https://www.mathnet.ru/eng/cmfd/v15/p36
This publication is cited in the following 4 articles:
Irene Benedetti, Luisa Malaguti, Manuel D.P. Monteiro Marques, “Differential equations with maximal monotone operators”, Journal of Mathematical Analysis and Applications, 539:1 (2024), 128484
M. M. Kulmanakova, V. V. Obukhovskii, E. L. Ulyanova, “Obobschennaya granichnaya zadacha dlya upravlyaemoi sistemy s obratnoi svyazyu i beskonechnym zapazdyvaniem”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:121 (2018), 44–64
Monographs and Research Notes in Mathematics, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions, 2016, 339
Benedetti I., Malaguti L., Taddei V., “Nonlocal Semilinear Evolution Equations Without Strong Compactness: Theory and Applications”, Bound. Value Probl., 2013, 60
Citation in format AMSBIB
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