华东师范大学学报(自然科学版)

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p-拉普拉斯时滞平均曲率方程的同宿解(英)

孔凡超[1] ,李迅[2] ,鲁世平[3]   

  1. 1. 湖南师范大学 数学系, 长沙 410081;2. 安徽师范大学 数学计算机科学学院, 安徽 芜湖241000;3. 南京信息工程大学 数学与统计学院, 南京 210044
  • 收稿日期:2015-06-09 出版日期:2016-07-25 发布日期:2016-09-29
  • 通讯作者: 孔凡超, 男, 硕士研究生, 研究方向为泛函微分方程. E-mail: fanchaokong88@sohu.com.
  • 基金资助:

    国家自然科学基金(11271197)

Homoclinic solutions for prescribed mean curvature p-Laplacian equations with delays

KONG Fan-chao[1] , LI-Xun[2] , LU Shi-ping[3]   

  1. 1. Department of Mathematics, Hunan Normal University, Changsha 410081, China;
    2. School of Mathematics and Computer Science, Anhui Normal University, Wuhu Anhui 241000, China;
    3. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • Received:2015-06-09 Online:2016-07-25 Published:2016-09-29

摘要:

本文运用Mawhin重合度拓展定理和一些分析方法研究了一类Rayleigh型 p-拉普拉斯时滞平均曲率方程 2kT-周期解的存在性, 证明了周期解序列存在极限, 且极限点就是所研究方程的同宿解. 最后, 我们给出例子来验证文章结论的有效性.

关键词: 平均曲率方程, 同宿解, 拓展定理, p-拉普拉斯方程, 时滞

Abstract:

In this paper, by applying Mawhin’s continuation theorem, some sufficient conditions on the existence of 2kT-periodic solutions for a kind of prescribed mean curvature Rayleigh p-Laplacian equation with delays are given. Then the existence of nontrivial homoclinic solutions for prescribed mean curvature Rayleigh p-Laplacian equation with delays is obtained. At last, an example is also given to illustrate the application of our main results.

Key words: prescribed mean curvature equation, homoclinic solutions, continuation theorem, p-Laplacian equation, delay