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Homoclinic solutions for a second-order singular differential equation

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Abstract

In this paper, the problem of existence of homoclinic solutions is studied for the second-order singular differential equation

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

where \(f,g,h,\alpha : R\rightarrow R\) are continuous and \(\alpha (t+T)\equiv \alpha (t)\) for all \(t\in R\). Using the continuation theorem of coincidence degree theory given by Mawhin and Manásevich, a new result on the existence of homoclinic solutions to the equation is obtained.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, 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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Lu, S., Jia, X. Homoclinic solutions for a second-order singular differential equation. J. Fixed Point Theory Appl. 20, 101 (2018). https://doi.org/10.1007/s11784-018-0575-9

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