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Viability theory and fuzzy differential equations. (English) Zbl 1074.34009
The authors present a new viability theory for differential inclusions and establish new existence results for fuzzy differential equations. In the literature, viability theory is presented for first-order differential inclusions where the nonlinearity is bounded. But this paper represents a general theory and removes the boundedness assumption by assuming the existence of a maximal solution to an approximate set of differential equations.
MSC:
34A60Differential inclusions
26E50Fuzzy real analysis
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34G25Evolution inclusions