摘要
本文考虑二阶哈密顿系统-ü(t)+L(t)u(t)=μu(t)+W_(u)(t,u(t))(t∈R)(HS)同宿轨道解的存在性。其中W∈C^(1)(R×R^(N),R),L(t)∈C(R,R^(N^2))是对称矩阵函数,且满足强制条件(L),μ是参数,且位于(HS)对应的特征值问题-ü(t)+L(t)u(t)=λu(t)的某两个特征值之间,即λ_(k)<μ<λ_(k+1)。再假设W在无穷远处满足次二次增长条件,通过临界点理论和指标理论,可证明(HS)的多重同宿轨道解的存在性。
In this paper,the existence and multiplicity of homoclinic solutions for second-order Hamiltonian System of the form-ü(t)+L(t)u(t)=μu(t)+W_(u)(t,u(t))(t∈R)(HS)are studied,where W∈C^(1)(R×R^(N),R)is subquadratic at infinity,L(t)∈C(R,R^(N2))is a symmetric matrix-valued function satisfying coercive condition(L),andμis a parameter between two eigenvalues of the corresponding eigenvalue problem for(HS),i.e.λ_(k)<μ<λ_(k+1).By critical point theory and index theory,the existence and multiplicity of homoclinic solutions for(HS)are proved.
作者
颜章建
李成岳
张卫杰
YAN Zhangjian;LI Chengyue;ZHANG Weijie(College of Science,Minzu University of China,Beijing 100081,China;The Affiliated High School to the Minzu University of China,Beijing 100081,China)
出处
《中央民族大学学报（自然科学版）》
2021年第2期12-18,共7页
Journal of Minzu University of China(Natural Sciences Edition)
关键词
哈密顿系统
临界点
指标定理
同宿轨道
Hamiltonian system
critical point
index theory
homoclinic solution
