[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()

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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

Author(s):

Ding Jian¹;  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

Keywords:

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

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.

References:

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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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