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Multiple Positive Periodic Solutions for Second-Order Differential Equations with a Singularity

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Abstract

In this paper, we obtain the existence of multiple positive periodic solutions for second-order differential equations with a singularity of the form

$$\begin{aligned} x''(t)+f\bigl(t,x(t)\bigr)x'(t)+g \bigl(x(t)\bigr)=p(t)=p(t+T) \end{aligned}$$

by means of the continuation theorem of coincidence degree theory. This type of equations can be used to describe the forced oscillator driven in Lennard-Jones potential. As an application, an examples is given, and the numerical periodic solutions for this example is obtained by applying Maple software.

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  1. School of Sciences, Hubei University of Technology, Wuhan, 430068, China

    Desheng Tian

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Tian, D. Multiple Positive Periodic Solutions for Second-Order Differential Equations with a Singularity. Acta Appl Math 144, 1–10 (2016). https://doi.org/10.1007/s10440-015-0030-5

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  • DOI: https://doi.org/10.1007/s10440-015-0030-5

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