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Approximate solutions, existence, and uniqueness of the Cauchy problem of fuzzy differential equations. (English) Zbl 0861.34040

The authors study the Cauchy problem \(x'(t)= f(t,x(t))\), \(x(t_0)= x_0\) for fuzzy differential equations. First the authors show that if \(x_n(t)\) is a solution to an approximate differential equation and \(x_n(t)\) converges uniformly, then the limit function is a solution to the Cauchy problem. Then they give an existence and uniqueness theorem for a solution to the Cauchy problem, which generalizes the corresponding theorem of O. Kaleva [Fuzzy Sets Syst. 24, 301-317 (1987; Zbl 0646.34019)]. (Also submitted to MR).
Reviewer: O.Kaleva (Tampere)

MSC:

34G20 Nonlinear differential equations in abstract spaces
34A45 Theoretical approximation of solutions to ordinary differential equations

Citations:

Zbl 0646.34019
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