zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

34G25Evolution inclusions
34A60Differential inclusions
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
[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