Ibrahim, A. G.; Gomaa, A. G. Extremal solutions of classes of multivalued differential equations. (English) Zbl 1037.34052 Appl. Math. Comput. 136, No. 2-3, 297-314 (2003). The paper is concerned with the existence of extremal solutions to a class of multivalued boundary value problems and evolution inclusion with m-accretive operators. Recently, similar problems have been considered in many papers. For example, more deeper results of such kind can be found in the book by Sh. Hu and N. S. Papageorgiou [Handbook of multivalued analysis. Volume II: Applications. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0943.47037)], and in the references therein. Reviewer’s remark: The paper contains a lot of inaccuracies. For example 1. the space \(E\) must be separable; 2. according to the proof of theorem 4 the function \(x(t)\) is measurable only, so the definition 3 of a solution is incorrect, etc., theorem 11 contains nothing new since the mild solution sets coincide with the integral solution sets. Reviewer: A. A. Tolstonogov (Irkutsk) Cited in 1 ReviewCited in 4 Documents MSC: 34G25 Evolution inclusions 34A60 Ordinary differential inclusions 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:extreme solution; boundary value problem; m-accretive operator; mild solution; compact semigroup PDF BibTeX XML Cite \textit{A. G. Ibrahim} and \textit{A. G. Gomaa}, Appl. Math. Comput. 136, No. 2--3, 297--314 (2003; Zbl 1037.34052) Full Text: DOI References: [1] M. Benamara, Point Extremaux, Multi-applications et Fonctionelles Integrales, These de 3eme Cycle, Universite de Grenoble, 1975 [2] Bressan, A.; Colombo, G., Extensions and selections of maps with decomposable values, Studia math., 90, 69-86, (1988) · Zbl 0677.54013 [3] Browen, L.D.; Purves, R., Measurable selection of extrema, Ann. statist., 1, 902-912, (1973) · Zbl 0265.28003 [4] Cichon, M., Multivalued perturbations of m-accretive differential inclusions in a non-separable Banach space, Ann. soc. math. polonae, 17, 11-17, (1992) · Zbl 0770.34015 [5] F.S. DeBlasi, G. Pianigiani, Solution sets of boundary value problems for nonconvex differential inclusions, Centro V. Volterra, University of Rome, 1992 (preprint 115) [6] Evans, L.C., Nonlinear evolution equations in an arbitrary Banach space, Isreal J. math., 26, 1-42, (1977) · Zbl 0349.34043 [7] Ibrahim, A.G., Functional evolution equations with nonconvex lower semicontinuous multivalued perturbations, Int. J. math. math. sci. (USA), 21, 1, 165-170, (1998) · Zbl 0894.34070 [8] Papageorgiou, N.S., Convergence theorems for Banach space valued integrable multifunctions, J. math. sci., 10, 433-442, (1987) · Zbl 0619.28009 [9] Papageorgiou, N.S., On measurable multifunction with applications to random multivalued equations, Math. japon., 32, 437-464, (1987) · Zbl 0634.28005 [10] Papageorgiou, N.S., Boundary value problems for nonconvex differential inclusions, J. math. anal. appl., 185, 1, 146-160, (1994) · Zbl 0817.34009 [11] Tolstonogov, A.A., Extremal selections of multivalued mappings and the bang – bang principle for evolution inclusions, Soviet math. dokl., 43, 2, 481-485, (1991) · Zbl 0784.54024 [12] Truong, Xuan Duc Ha, Differential inclusions governed by convex and nonconvex perturbation of a sweeping process, Bollettino U.M.I, 7, 8-B, 349-360, (1994) · Zbl 0804.34016 [13] Vrabie, I.L., Compactness methods for nonlinear evolutions, Pitman monographs surveys pure appl. math., 32, (1987) · Zbl 0721.47050 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.