一类带参数的二阶次二次哈密顿系统多重同宿轨道解的存在性研究  

Multiple Homoclinic Solutions for a Class of Subquadratic Hamiltonian Systems with a Parameter

作　　者：颜章建 李成岳[1] 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)

机构地区：[1]中央民族大学理学院,北京100081 [2]中央民族大学附属中学,北京100081

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)

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.

关 键 词：哈密顿系统 临界点 指标定理 同宿轨道 

分 类 号：O175[理学—数学]