An existence and uniqueness theorem to the Cauchy problem for generalised set differential equations (Q2849209)
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scientific article; zbMATH DE number 6208683
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence and uniqueness theorem to the Cauchy problem for generalised set differential equations |
scientific article; zbMATH DE number 6208683 |
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17 September 2013
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set-valued mapping
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Hukuhara derivative
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generalized derivative
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set differential equation
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existence and uniqueness theorems
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An existence and uniqueness theorem to the Cauchy problem for generalised set differential equations (English)
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The authors consider the concept of generalized differentiability for set-valued mappings and study the corresponding generalized set differential equations (GSDE). They prove existence and uniqueness results for the GSDE. They give many interesting examples where they explicitly discuss the solutions of a Hukuhara derivative SDE and the solutions of a GSDE. The examples explain how for solutions of a Hukuhara derivative SDE the diameter of the set increases, whereas for the generalized SDE, the solutions can increase, decrease or remain constant on various intervals of time.
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