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Zbl 1037.34052
Ibrahim, A. G.; Gomaa, A. G.
Extremal solutions of classes of multivalued differential equations. (English)
[J] Appl. Math. Comput. 136, No. 2-3, 297-314 (2003). ISSN 0096-3003

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.\par 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.
[A. A. Tolstonogov (Irkutsk)]

MSC 2000:: *34G25 Evolution inclusions
34A60 ODE with multivalued right-hand sides
34B15 Nonlinear boundary value problems of ODE

Keywords: extreme solution; boundary value problem; m-accretive operator; mild solution; compact semigroup

Citations: Zbl 0943.47037

Cited in: Zbl 1249.34053

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