| 一类具有奇性的时滞平均曲率方程周期解的存在性问题 |
| |
| 引用本文： | 郑淑媛,孔凡超,鲁世平.一类具有奇性的时滞平均曲率方程周期解的存在性问题[J].四川大学学报(自然科学版),2016,53(3):490-496. |
| |
| 作者姓名： | 郑淑媛 孔凡超 鲁世平 |
| |
| 作者单位： | 安徽师范大学数计学院,安徽师范大学数计学院,南京信息工程大学数理学院 |
| |
| 摘 要： | 本文研究了如下具有奇性的Li\''{e}nard型时滞平均曲率方程$$(\frac{u''(t)}{\sqrt{1+(u''(t))^2}})''+f(u(t))u''(t)+g( u(t-\gamma))=e(t)$$的周期解存在性问题. 运用Mawhin重合度扩展定理, 获得了该方程至少存在一个$T$-周期正解的新结果, 最后给出一个例子来验证文章主要结论的有效性. 本文的研究丰富了时滞平均曲率方程的内容.
|
| 关 键 词： | 周期解 重合度拓展定理 Li\''{e}nard型平均曲率方程 奇性 |
| 收稿时间： | 2015/6/29 0:00:00 |
| 修稿时间： | 2015/9/17 0:00:00 |
Existence of positive periodic solutions for a delay prescribed mean curvature equation with a singularity |
| |
| ZHENG Shu-Yuan,KONG Fan-Chao and LU Shi-ing.Existence of positive periodic solutions for a delay prescribed mean curvature equation with a singularity[J].Journal of Sichuan University (Natural Science Edition),2016,53(3):490-496. |
| |
| Authors: | ZHENG Shu-Yuan KONG Fan-Chao and LU Shi-ing |
| |
| Institution: | Department of Mathematics, Anhui Normal University,Department of Mathematics, Anhui Normal University and College of Mathematics and Statistics, NUIST |
| |
| Abstract: | In this paper, we study the existence of periodic solutions to the following prescribed mean curvature Li\''{e}nard equation with a singularity and a deviating argument $$(\frac{u''(t)}{\sqrt{1+(u''(t))^2}})''+f(u(t))u''(t)+g( u(t-\gamma))=e(t)$$ And by applying Mawhin''s continuation theorem, a new result on the existence of positive $T-$periodic solution for this equation is obtained. An example is given
to illustrate the effectiveness of our results. Our research
enriches the contents of prescribed mean curvature equations. |
| |
| Keywords: | Positive periodic solutions Continuation theorem Prescribed mean curvature equation Singularity |
|
| 点击此处可从《四川大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《四川大学学报(自然科学版)》下载免费的PDF全文 |
