Remarks on Peano-like theorems for fuzzy differential equations
Kloeden, P.E. (1991) Remarks on Peano-like theorems for fuzzy differential equations. Fuzzy Sets and Systems, 44 (1). pp. 161-163.
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The validity of the classical Peano theorem is noted for differential equations on the metric space (En, dp) of normal fuzzy convex sets in Rn, where dp is the p-th mean of the Hausdorff distances between corresponding level sets. This contrasts with differential equations on the space (En, D) where D is the max metric, which is not locally compact so more than just continuity is required to ensure the existence of solutions. Some additional properties, differing from that given by Kaleva, are mentioned.
|Publication Type:||Journal Article|
|Murdoch Affiliation:||School of Mathematical and Physical Sciences|
|Copyright:||© 1991 Published by Elsevier B.V.|
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