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2021 Periodic solutions of superlinear and sublinear state-dependent discontinuous differential equations
Juan J. Nieto, José M. Uzal
Topol. Methods Nonlinear Anal. 58(1): 79-96 (2021). DOI: 10.12775/TMNA.2021.016

Abstract

A classical, second-order differential equation is considered with state-dependent impulses at both the position and its derivative. This means that the instants of impulsive effects depend on the solutions and they are not fixed beforehand, making the study of this problem more difficult and interesting from the real applications point of view. The existence of periodic solutions follows from a transformation of the problem into a planar system followed by a study of the Poincaré map and the use of some fixed point theorems in the plane. Some examples are presented to illustrate the main results.

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Juan J. Nieto. José M. Uzal. "Periodic solutions of superlinear and sublinear state-dependent discontinuous differential equations." Topol. Methods Nonlinear Anal. 58 (1) 79 - 96, 2021. https://doi.org/10.12775/TMNA.2021.016

Information

Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2021.016

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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