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Extremal solutions of classes of multivalued differential equations. (English) Zbl 1037.34052
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 {\it Sh. Hu} and {\it 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.

##### MSC:
 34G25 Evolution inclusions 34A60 Differential inclusions 34B15 Nonlinear boundary value problems for ODE
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##### 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, No. 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, No. 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, No. 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, No. 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