[1] Ding Jian, Feng Guizhen, Zhang Fubao, et al. Multiple homoclinics in a non-periodic Hamiltonian system [J]. Journal of Southeast University (English Edition), 2010, 26 (4): 642-646. [doi:10.3969/j.issn.1003-7985.2010.04.029]

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Multiple homoclinics in a non-periodic Hamiltonian system()

非周期Hamilton系统的多同宿轨

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

26

Issue:

2010 4

Page:

642-646

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2010-12-30

Info

Title:

Multiple homoclinics in a non-periodic Hamiltonian system

非周期Hamilton系统的多同宿轨

Author(s):

Ding Jian^{1, 2}, Feng Guizhen³, Zhang Fubao¹

¹ Department of Mathematics, Southeast University, Nanjing 211189, China
²College of Math and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China
³ College of Arts and Science, Nanjing Institute of Industry Technology, Nanjing 210046, China

丁建^{1, 2}, 冯桂珍³, 张福保¹

¹ 东南大学数学系, 南京 211189; ²南京信息工程大学数理学院, 南京 210044; ³南京工业职业技术学院人文数理学院, 南京 210046

Keywords:

Hamiltonian system;  homoclinic orbits;  (C)-condition;  asymptotical linearity;  generalized mountain pass theorem

Hamilton系统;  同宿轨;  (C)-条件;  渐近线性;  广义山路定理

PACS:

O175

DOI:

10.3969/j.issn.1003-7985.2010.04.029

Abstract:

This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system (¨overz)-L(t)z+W_z(t, z)=0, where L∈C(R, R^N22)is a symmetric matrix-valued function and W(t, z)∈C¹1(R×R^N, R)is a nonlinear term. Since there are no periodic assumptions on L(t)and W(t, z)in t, one should overcome difficulties for the lack of compactness of the Sobolev embedding. Moreover, the nonlinearity W(t, z)is asymptotically linear in z at infinity and the system is allowed to be resonant, which is a case that has never been considered before. By virtue of some generalized mountain pass theorem, multiple homoclinic orbits are obtained.

研究了二阶Hamilton系统(¨overz)-L(t)z+W_z(t, z)=0多个同宿轨的存在性, 其中L∈C(R, R^N2)是一对称矩阵值函数, W(t, z)∈C¹(R×R^N, R)是非线性项.由于L(t)和W(t, z)关于t没有周期性假设, 需要克服Sobolev嵌入缺乏紧性的困难.而且, 这里非线性项W(t, z)关于z在无穷远处是渐进线性的且系统允许出现共振, 这一情形之前未被考虑过.借助于广义的山路定理, 得到了多个同宿轨.

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Memo

Memo:

Biographies: Ding Jian(1978—), male, doctor; Zhang Fubao(corresponding author), male, doctor, professor, zhangfubao@seu.edu.cn.
Citation: Ding Jian, Feng Guizhen, Zhang Fubao.Multiple homoclinics in a non-periodic Hamiltonian system[J].Journal of Southeast University(English Edition), 2010, 26(4):642-646.

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