Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima

1 October 2000

journal article
research article
Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Vol. 130 (5) , 1103-1118
https://doi.org/10.1017/s0308210500000597

Abstract

We study the stability of periodic solutions of the scalar delay differential equation where f(t) is a periodic forcing term and δ,p∈R. We study stability in the first approximation showing that the non-smooth equation (*) can be linearized along some ‘non-singular’ periodic solutions. Then the corresponding variational equation together with the Krasnosel'skij index are used to prove the existence of multiple periodic solutions to (*). Finally, we apply a generalization of Halanay's inequality to establish conditions for global attractivity in equations with maxima.

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