p-拉普拉斯时滞平均曲率方程的同宿解(英)

doi:10.3969/j.issn.1000-5641.2016.04.006

华东师范大学学报(自然科学版)

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. 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. 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/Abstract

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

孔凡超,李迅,鲁世平. p-拉普拉斯时滞平均曲率方程的同宿解(英)[J]. 华东师范大学学报(自然科学版), doi: 10.3969/j.issn.1000-5641.2016.04.006.

KONG Fan-chao, LI-Xun, LU Shi-ping. Homoclinic solutions for prescribed mean curvature p-Laplacian equations with delays[J]. Journal of East China Normal University(Natural Sc, doi: 10.3969/j.issn.1000-5641.2016.04.006.

参考文献

[ 1 ] BONHEURE D, HABETS P, OBERSNEL F, et al. Classical and non-classical solutions of a prescribed curvature equation [J]. J Differ Equ, 2007, 243(2): 208-237.
[ 2 ] PAN H J. One-dimensional prescribed mean curvature equation with exponential nonlinearity [J]. Nonlinear Anal, 2009, 70(2): 999-1010.
[ 3 ] BENEVIERIA P, DO´O J, DE MEDEIROS E. Periodic solutions for nonlinear systems with mean curvature-like operators [J]. Nonlinear Anal, 2006, 65(7): 1462-1475.
[ 4 ] LI W S, LIU Z L. Exact number of solutions of a prescribed mean curvature equation [J]. J Math Anal Appl, 2010, 367(2): 486-498.
[ 5 ] HABETS P, OMARI P. Multiple positive solutions of a one dimensional prescribed mean curvature problem [J]. Commun Contemp Math, 2007, 95: 701-730.
[ 6 ] FENG M Q. Periodic solutions for prescribed mean curvature Li´enard equation with a deviating argument [J]. Nonlinear Anal: Real World Appl, 2012, 13(3): 1216-1223.
[ 7 ] LIANG Z T, LU S P. Homoclinic solutions for a kind of prescribed mean curvature Duffing-type equation [J]. Adv Differ Equ, 2013, 2013: 279.
[ 8 ] LZYDOREK M, JANCZEWSKA J. Homoclinic solutions for a class of the second order Hamiltonian systems [J]. J Differ Equ, 2005, 219: 375-389.
[ 9 ] RABINOWITZ P. Homoclinic orbits for a class of Hamiltonian systems [J]. Proc R Soc Edinb A, 1990, 114: 33-38.
[10] TANG X H, XIAO L. Homoclinic solutions for ordinary p-Laplacian systems with a coercive potential [J]. Nonlinear Anal, 2009, 71: 1124-1132.
[11] LU S P. Homoclinic solutions for a class of second-order p-Laplacian differential systems with delay [J]. Nonlinear Anal: Real World Appl, 2011, 12: 780-788.
[12] ZHENG M, LI J. Nontrivial homoclinic solutions for prescribed mean curvature Rayleigh equations [J]. Adv Differ Equ, 2015, 2015: 77.
[13] LI Z Y, AN T Q, GE W G. Existence of periodic solutions for a prescribed mean curvature Li´enard p-Laplaceian equation with two delays [J]. Adv Differ Equ, 2014, 2014: 290.
[14] WANG D. Existence and uniqueness of periodic solution for prescribed mean curvature Rayleigh type p-Laplacian equation [J]. J Appl Math Comput, 2014, 46(1): 181-200.
[15] LU S P, GE W G. Periodic solutions for a kind of second order differential equations with multiple with deviating arguments [J]. Appl Math Comput, 2003, 146: 195-209.
[16] GAINES R E, MAWHIN J L. Coincidence Degree and Nonlinear Differential Equation [M]. New York: Springer-Verlag, 1977.

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p-拉普拉斯时滞平均曲率方程的同宿解(英)

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

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