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Existence and Uniqueness of Homoclinic Solution for a Rayleigh Equation with a Singularity

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Abstract

The problem of homoclinic solutions is considered for a singular Rayleigh equation

$$\begin{aligned} x''(t)+f(x'(t))-g(x(t))-\frac{\alpha (t)x(t)}{1-x(t)}=h(t), \end{aligned}$$

where \(f,g,h,\alpha : R\rightarrow R\) are continuous and \(\alpha (t)\) is \(T-\)periodic. By using a continuation theorem of coincidence degree principle, some new results on the existence and uniqueness of homoclinic solution to the equation are obtained.

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Acknowledgements

The authors are grateful to the referee for the careful reading of the paper and for useful suggestions.

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  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Shiping Lu & Xuewen Jia

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  1. Shiping Lu
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  2. Xuewen Jia
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Correspondence to Shiping Lu.

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This work was completed with the support of the NSF of China (No. 11271197).

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Lu, S., Jia, X. Existence and Uniqueness of Homoclinic Solution for a Rayleigh Equation with a Singularity. Qual. Theory Dyn. Syst. 19, 17 (2020). https://doi.org/10.1007/s12346-020-00357-6

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  • DOI: https://doi.org/10.1007/s12346-020-00357-6

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