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

Wu, Congxin; Song, Shiji; Lee, E. Stanley

J. Math. Anal. Appl. 202, No. 2, 629-644 (1996).

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

Keywords:

Cauchy problem; fuzzy differential equations; existence; uniqueness

Citations:

Zbl 0646.34019