Extremal solutions of classes of multivalued differential equations. (English) Zbl 1037.34052

Ibrahim, A. G.; Gomaa, A. G.

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)

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

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