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The Cauchy problem for continuous fuzzy differential equations. (English) Zbl 0929.34005
Summary: The author proves a version of the classical Peano theorem for the initial value problem for a fuzzy differential equation in the metric space of normal fuzzy convex sets with the distance given by the maximum of the Hausdorff distances between level sets.

34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
03E75Applications of set theory
28E10Fuzzy measure theory
34G20Nonlinear ODE in abstract spaces
Full Text: DOI
[1] Agarwal, R. P.; Lakshmikantham, V.: Uniqueness and nonuniqueness criteria for ordinary differential equations. (1993) · Zbl 0785.34003
[2] Brown, A.; Pearcy, C.: An introduction to analysis. (1995) · Zbl 0820.00003
[3] Coddington, E. A.; Levinson, N.: Theory of ordinary differential equations. (1955) · Zbl 0064.33002
[4] Diamond, P.; Kloeden, P.: Metric spaces of fuzzy sets. (1994) · Zbl 0873.54019
[5] Hartman, P.: Ordinary differential equations. (1964) · Zbl 0125.32102
[6] Kaleva, O.: Fuzzy differential equations. Fuzzy sets and systems 24, 301-307 (1987) · Zbl 0646.34019
[7] Kaleva, O.: The Cauchy problem for fuzzy differential equations. Fuzzy sets and systems 35, 389-396 (1990) · Zbl 0696.34005
[8] Kloeden, P. E.: Remarks on Peano-like theorems for fuzzy differential equations. Fuzzy sets and systems 44, 161-163 (1991) · Zbl 0742.34058
[9] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S.: Monotone iterative techniques for nonlinear differential equations. (1985) · Zbl 0658.35003
[10] Lakshmikantham, V.; Leela, S.: Nonlinear differential equations in abstract spaces. (1981) · Zbl 0456.34002
[11] Seikkala, S.: On the fuzzy initial value problem. Fuzzy sets and systems 24, 319-330 (1987) · Zbl 0643.34005