Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains (Q2087426)

The authors of this illuminating paper show how direct applications of Brouwer's classical fixed point theorem lead to several results of nonlinear analysis and the theory of ordinary differantial equations involving the existence of equilibrium points and periodic solutions. In particular, they provide a positive answer to a question which has recently been raised by \textit{J. Á. Cid} and \textit{J. Mawhin} [J. Fixed Point Theory Appl. 25, No. 1, Paper No. 38, 12 p. (2023; Zbl 07638844)].