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Regularity of solution sets for differential inclusions quasi-concave in a parameter. (English) Zbl 0944.34008

Summary: The concept of quasi-concavity is extended to multifunctions. It is then shown that if the velocity of a differential inclusion is regularly quasi-concave in a parameter, the solution set and attainability set are also dependent upon the parameter in like manner. The result is applied to give a vastly improved notion of fuzzy differential equations.

MSC:

34A60 Ordinary differential inclusions
34G20 Nonlinear differential equations in abstract spaces
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