一类Rayleigh型 $p-$Laplacian平均曲率方程周期解存在唯一性

Existence and uniqueness of periodic solutions for prescribed mean curvature Rayleigh $p-$Laplacian equation

摘要:

运用重合度理论和一些新的分析方法探讨了一类 Rayleigh型 $p-$Laplacian平均曲率 方程 \begin{displaymath} \left(\varphi_{p}\left(\frac{x'(t)}{\sqrt{1+(x'(t))^{2}}}\right)\right)'+f(x'(t))+g(x(t-\tau (t)))=e(t) \end{displaymath} 周期解存在性与唯一性问题, 得到了一些相应的新结果并举例说明其结果的有效性.

Abstract:

In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study the existence and uniqueness of periodic solutions for prescribed mean curvature Rayleigh $p-$Laplacian equation \begin{displaymath} \left(\varphi_{p}\left(\frac{x'(t)}{\sqrt{1+(x'(t))^{2}}}\right)\right)'+f(x'(t))+g(x(t-\tau (t)))=e(t). \end{displaymath} Some new results are obtained. Furthermore, a numerical example demonstrates the validity of the main results.