Homoclinic orbits of first order discrete Hamiltonian systems with super linear terms

被引：7

作者：

Chen WenXiong ^{[1
]}

Yang MinBo ^{[2
,3
]}

Ding YanHeng ^{[2
]}

机构：

[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China

[3] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 12期

基金：

中国国家自然科学基金;

关键词：

homoclinic orbits; first order discrete Hamiltonian systems; super linear; critical points; MULTIPLE PERIODIC-SOLUTIONS; DIFFERENCE-EQUATIONS; DISCONJUGACY; EXISTENCE; SYMMETRY;

D O I：

10.1007/s11425-011-4276-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the first order discrete Hamiltonian systems {x(1)(n + 1) - x(1)(n) = - H(x2) (n, x(n)), x(2)(n) - x(2)(n - 1) = H(x1) (n, x(n)), where x(n) = ((x1(n))(x2(n)) is an element of R(2N), H(n, z) = 1/2 S(n) z . z + R(n, z) is periodic in n and superlinear as |z| -> infinity. We prove the existence and infinitely many (geometrically distinct) homoclonic orbits of the system by critical point theorems for strongly indefinite functionals.

引用

页码：2583 / 2596

页数：14

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