English

Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains

Classical Analysis and ODEs 2022-03-03 v1

Abstract

We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a general approach for arbitrary bound sets and present applications to the case of convex and star-shaped domains. We also provide an answer to a question raised in a recent paper of Cid and Mawhin.

Keywords

Cite

@article{arxiv.2203.00950,
  title  = {Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains},
  author = {Guglielmo Feltrin and Fabio Zanolin},
  journal= {arXiv preprint arXiv:2203.00950},
  year   = {2022}
}

Comments

22 pages, 3 figures