Ibrahim, A. G.; Aladsani, F. Convex sweeping processes with noncompact perturbations and with delay in Banach spaces. (English) Zbl 1470.34055 Abstr. Appl. Anal. 2016, Article ID 3853205, 13 p. (2016). Summary: We prove two results concerning the existence of solutions for functional differential inclusions that are governed by sweeping processes, with noncompact valued perturbations in Banach spaces. Indeed, we have two goals. The first is to give a technique that allows considering sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time. The second is to give a technique to overcome the arising problem from the nonlinearity of the normalized mappings, when we deal with sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time and state. MSC: 34A60 Ordinary differential inclusions 34G20 Nonlinear differential equations in abstract spaces 34K09 Functional-differential inclusions 49J52 Nonsmooth analysis × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Moreau, J. J., Evolution problem associated with a moving convex set in a Hilbert space, Journal of Differential Equations, 26, 3, 347-374, (1977) · Zbl 0356.34067 · doi:10.1016/0022-0396(77)90085-7 [2] Aitalioubrahim, M., On noncompact perturbation of nonconvex sweeping process, Commentationes Mathematicae Universitatis Carolinae, 53, 1, 65-77, (2012) · Zbl 1249.34183 [3] Al-Adsani, F. A.; Ibrahim, A. G., Noncompact perturbation of sweeping process with delay in Banach spaces, International Journal of Mathematics and Mathematical Sciences, 2013, (2013) · Zbl 1286.34086 · doi:10.1155/2013/567094 [4] Bounkhel, M.; Thibault, L., Non-convex sweeping process and prox-regular in Hilbert spaces, Journal of Nonlinear and Convex Analysis, 6, 359-374, (2005) · Zbl 1086.49016 [5] Bounkhel, M.; Al-Yusof, R., First and second order convex sweeping processes in reflexive smooth banach spaces, Set-Valued and Variational Analysis, 18, 2, 151-182, (2010) · Zbl 1200.34067 · doi:10.1007/s11228-010-0134-z [6] Bounkhel, M.; Castaing, C., State dependent sweeping process in p-uniformly smooth and q-uniformly convex Banach spaces, Set-Valued and Variational Analysis, 20, 2, 187-201, (2012) · Zbl 1262.34072 · doi:10.1007/s11228-011-0186-8 [7] Ibrahim, A. G.; AL-Adsani, F. A., Second order evolutions inclusions governed by sweeping process in Banach spaces, Le Matematiche, 64, 2, 17-39, (2009) · Zbl 1214.34050 [8] Noel, J.; Thibault, L., Nonconvex sweeping process with a moving set depending on the state, Vietnam Journal of Mathematics, 42, 4, 595-612, (2014) · Zbl 1315.34068 · doi:10.1007/s10013-014-0109-8 [9] Thibault, L., Sweeping process with regular and nonregular sets, Journal of Differential Equations, 193, 1, 1-26, (2003) · Zbl 1037.34007 · doi:10.1016/S0022-0396(03)00129-3 [10] Castaing, C.; Ibrahim, A. G.; Yarou, M., Some contributions to nonconvex sweeping process, Journal of Nonlinear and Convex Analysis, 10, 1, 1-20, (2009) · Zbl 1185.34017 [11] A. M. Gomaa, Relaxation problems involving second order differential inclusions, Abstract and Applied Analysis, 2013, (2013) · Zbl 1272.49025 · doi:10.1155/2013/792431 [12] Alber, Y. I., Generalized projection operators in Banach spaces: properties and applications, Functional Differential Equations, 1, 1-21, (1994) · Zbl 0882.47046 [13] Takahashi, W., Nonlinear Functional Analysis, (2000), Yokohama Publishers · Zbl 0997.47002 [14] Deville, R.; Godefroy, G.; Zizler, V., Smoothness and Renormings in Branch Spaces. Smoothness and Renormings in Branch Spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics, (1993), Harlow, UK: Longman Scientific & Technical, Harlow, UK · Zbl 0782.46019 [15] Zhu, Q. J., On the solution set of differential inclusions in Banach space, Journal of Differential Equations, 93, 2, 213-237, (1991) · Zbl 0735.34017 · doi:10.1016/0022-0396(91)90011-w [16] Aubin, J. P.; Cellina, A., Differential Inclusions: Set-Valued Maps and Viability Theory, (1984), Berlin, Germany: Springer, Berlin, Germany · Zbl 0538.34007 [17] Thibault, L., Propriétés des sous-différentiels de fonctions localement lipschitziennes définies sur un espace de Banach séparable. Applications [Ph.D. thesis], (1976), Montpellier, France: University of Montpellier, Montpellier, France · Zbl 0343.46030 [18] Castaing, C.; Valadier, M., Convex Analysis and Measurable Multifunctions. Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, 580, (1977), Berlin, Germany: Springer, Berlin, Germany · Zbl 0346.46038 [19] Thibault, L., Requalarization of non-convex sweeping process in Hilbert spaces, Set-Valued Analysis, 16, 23, 319-333, (2008) · Zbl 1162.34010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.