On an extension of Rolle's theorem to locally convex spaces |
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Authors: | Marcelo H Kobayashi |
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Institution: | University of Hawai‘i at Manoa, Department of Mechanical Engineering, 2540 Dole Street, Holmes Hall 302, Honolulu, HI 96822, USA |
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Abstract: | This work concerns the extension of a weak form of the Rolle's theorem to locally convex spaces that satisfy an axiom of separation. The result provides a condition for asserting the uniqueness of a solution to nonlinear functional equations, including nonlinear integro-differential equations. We use the extended Rolle's theorem to prove the uniqueness of a solution to a nonlinear, fractional differential equation. |
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Keywords: | Rolle's theorem Uniqueness of solutions Fractional differential equations |
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