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)
Carathéodory solutions of fuzzy differential equations. (English) Zbl 1006.34054
Here, the authors establish a solution to fuzzy differential equations with right-hand side satisfying a Carathéodory condition. They do not quote important references, e.g. results due to {\it V. Lakshmikantham} and {\it Ram N. Mohapatra} [Fuzzy sets and fuzzy differential equations. K. Vajravelu (ed.), Differential equations and nonlinear mechanics. Proceedings of the international conference, Orlando, FL, USA. March 17-19, 1999. Dordrecht: Kluwer Academic Publishers. Math. Appl. Dordr. 528, 183-199 (2001; Zbl 0994.34046)].

34G20Nonlinear ODE in abstract spaces
Full Text: DOI
[1] Butnariu, D.: Measurability concepts for fuzzy mappings. Fuzzy sets and systems 31, 77-82 (1989) · Zbl 0664.28011
[2] Castaing, C.; Valadier, M.: Convex analysis and measurable multifunctions. (1977) · Zbl 0346.46038
[3] Diamond, P.; Kloeden, P. E.: Metric spaces of fuzzy sets: theory and applications. (1994) · Zbl 0873.54019
[4] Hukuhara, M.: Integration des applications measurables dont la valeur est compact convexe. Funkcialaj ekvacioj 10, 205-223 (1967) · Zbl 0161.24701
[5] Kaleva, O.: Fuzzy differential equations. Fuzzy sets and systems 24, 301-317 (1987) · Zbl 0646.34019
[6] Kaleva, O.: The Cauchy problem for fuzzy differential equations. Fuzzy sets and systems 35, 309-316 (1990) · Zbl 0696.34005
[7] A. Kandel, W.J. Byatt, Fuzzy differential equations, Proceedings of the International Conference on Cybernetics and Society, Tokyo, November 1978, pp. 1213--1216.
[8] Kloeden, P. E.: Remarks and Peano-like theorems for fuzzy differential equations. Fuzzy sets and systems 44, 161-163 (1991) · Zbl 0742.34058
[9] Puri, M. L.; Ralescu, D. A.: Differentials for fuzzy function. J. math. Anal. appl. 91, 552-558 (1983) · Zbl 0528.54009
[10] Puri, M. L.; Ralescu, D. A.: Fuzzy random variables. J. math. Anal. appl. 114, 409-422 (1986) · Zbl 0592.60004
[11] Papageorgiou, N.: On the theory of Banach space valued multifunctions. J. multivariate anal. 17, 185-206 (1985) · Zbl 0579.28009
[12] Seikkala, S.: On the fuzzy initial value problem. Fuzzy sets and systems 24, 319-330 (1987) · Zbl 0643.34005
[13] Xiaoping, Xue; Minghu, Ha; Ming, Ma: Random fuzzy number integrals in Banach spaces. Fuzzy sets and systems 66, 97-111 (1994) · Zbl 0845.46048
[14] Xiaoping, Xue; Xiaomin, Wang; Lizhong, Wu: On the convergence and representation of random fuzzy number integrals. Fuzzy sets and systems 103, 115-125 (1999) · Zbl 0960.28015