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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuous selections of solution sets to evolution equations
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by Vasile Staicu PDF
Proc. Amer. Math. Soc. 113 (1991), 403-413 Request permission

Abstract:

We prove the existence of a continuous selection of the multivalued map $\xi \to \mathcal {T}(\xi )$, where $\mathcal {T}(\xi )$ is the set of all weak (resp. mild) solutions of the Cauchy problem \[ \dot x(t) \in Ax(t) + F(t,x(t)),\quad x(0) = \xi \], assuming that $F$ is Lipschitzian with respect to $x$ and $- A$ is a maximal monotone map (resp. $A$ is the infinitesimal generator of a ${C_0}$-semigroup). We also establish an analog of Michael’s theorem for the solution sets of the Cauchy problem $\dot x(t) \in F(t,x(t)),\;x(0) = \xi$.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 403-413
  • MSC: Primary 49J24; Secondary 34A60, 47H04, 54C65
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1076580-7
  • MathSciNet review: 1076580