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Slowly oscillating solutions in a class of second-order discontinuous delayed systems

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Abstract

This paper investigates the dynamics of oscillations for a class of second-order discontinuous differential equations with time delay. First, by analyzing an implicit function which is determined by a crucial variable of initial values, the existence and uniqueness of a slowly oscillating periodic solution are discussed for equations without the first-degree linear term. And then, under some reasonable assumptions on parameters of the equivalent planar discontinuous systems, analytical conditions for the appearance of bounded slowly oscillating phenomenon are derived with the benefit of geometrical properties of generalized Poincaré maps. Finally, two numerical examples are provided to verify the existence of bounded slowly oscillating solutions. This work improves and extends some existing results of other researchers.

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Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, Zhejiang, People’s Republic of China

    Liping Li & Zhenjiang Zhao

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  1. Liping Li
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  2. Zhenjiang Zhao
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Correspondence to Liping Li.

Additional information

This work was supported by the National Natural Science Foundation of China under Grants 61473332 and 11571106.

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Li, L., Zhao, Z. Slowly oscillating solutions in a class of second-order discontinuous delayed systems. Nonlinear Dyn 94, 355–363 (2018). https://doi.org/10.1007/s11071-018-4363-2

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  • DOI: https://doi.org/10.1007/s11071-018-4363-2

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