Remarks on Peano-like theorems for fuzzy differential equations. (English) Zbl 0742.34058

Kloeden, P. E.

Fuzzy Sets Syst. 44, No. 1, 161-163 (1991).

From the author’s summary: “The validity of the classical Peano theorem is noted for differential equations on the metric space \(({\mathcal E}^ n,d_ p)\) of normal fuzzy convex sets in \(\mathbb{R}^ n\), where \(d_ p\) is the \(p\)-th mean of the Hausdorff distances between corresponding level sets.”.

Reviewer: K.S.Miller (Rye Brook)

MSC:

34G99	Differential equations in abstract spaces
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
54A40	Fuzzy topology
94D05	Fuzzy sets and logic (in connection with information, communication, or circuits theory)

Keywords:

classical Peano theorem; differential equations on the metric space; normal fuzzy convex sets

References:

[1]	Deimling, K., Ordinary Differential Equations in Banach Spaces, (Lecture Notes in Mathematics, 596 (1977), Springer: Springer Berlin) · Zbl 0555.60036
[2]	Diamond, P.; Kloeden, P. E., Characterization of compact sets of fuzzy sets, Fuzzy Sets and Systems, 29, 341-348 (1989) · Zbl 0661.54011
[3]	Diamond, P.; Kloeden, P. E., Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35, 241-250 (1990) · Zbl 0704.54006
[4]	Kaleva, O., Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987) · Zbl 0646.34019
[5]	Kaleva, O., The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, 389-396 (1990) · Zbl 0696.34005
[6]	Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319-330 (1987) · Zbl 0643.34005