Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains
Journal of Fixed Point Theory and Applications(2022)
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.
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Key words
Equilibrium points,periodic solutions,positively invariant sets,Brouwer fixed point theorem,convex sets,star-shaped sets
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