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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Monotonicity results for non-autonomous dynamical systems: The case of a general convex cone
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by Pedro Gajardo and Alberto Seeger
Proc. Amer. Math. Soc. 151 (2023), 771-778
DOI: https://doi.org/10.1090/proc/16226
Published electronically: November 10, 2022

Abstract:

Let $K$ be a closed convex cone in the state space $\mathbb {R}^n$. This note characterizes the $K$-monotonicity of a non-autonomous dynamical system $\dot x (t) = f(t,x(t))$ governed by a locally Lipschitz velocity field. We deviate from the classical literature in two important ways. Firstly, the velocity field $f$ is not required to be differentiable with respect to the state variables. And, secondly, the closed convex cone $K$ is allowed to be absolutely general. In particular, we impose neither pointedness, nor solidity.
References
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Bibliographic Information
  • Pedro Gajardo
  • Affiliation: Universidad Técnica Federico Santa María, Departamento de Matemática, Avenida España 1680, Valparaiso, Chile
  • MR Author ID: 718318
  • Email: pedro.gajardo@usm.cl
  • Alberto Seeger
  • Affiliation: University of Avignon, Department of Mathematics, 33 rue Louis Pasteur, 84000 Avignon, France
  • MR Author ID: 214067
  • ORCID: 0000-0003-3114-7817
  • Email: alberto.seeger@univ-avignon.fr
  • Received by editor(s): December 15, 2021
  • Received by editor(s) in revised form: June 6, 2022
  • Published electronically: November 10, 2022
  • Additional Notes: The first author was partially supported by FONDECYT Grant N 1200355 and BASAL FB210005, both programs from ANID-Chile.
  • Communicated by: Wenxian Shen
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 771-778
  • MSC (2020): Primary 34C12, 34A34, 34B18
  • DOI: https://doi.org/10.1090/proc/16226
  • MathSciNet review: 4520026