文章基本信息

标题：Homoclinic orbits for discrete Hamiltonian systems with subquadratic potential
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作者：Xiaoyan Lin ; Xianhua Tang
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：154
DOI：10.1186/1687-1847-2013-154
语种：English
出版社：Hindawi Publishing Corporation
摘要：In the present paper, we deal with the existence and multiplicity of homoclinic solutions of the second-order self-adjoint discrete Hamiltonian system △ [ p ( n ) △ u ( n − 1 ) ] − L ( n ) u ( n ) + ∇ W ( n , u ( n ) ) = 0 . Under the assumption that W ( n , x ) is of indefinite sign and subquadratic as x → + ∞ and p ( n ) and L ( n ) are N × N real symmetric positive definite matrices for all n ∈ Z , and that lim inf n → + ∞ [ n ν − 2 inf x = 1 ( L ( n ) x , x ) ] > 0 for some constant ν < 2 , we establish some existence criteria to guarantee that the above system has at least one or multiple homoclinic solutions by using Clark’s theorem in critical point theory. MSC:39A11, 58E05, 70H05.
关键词：homoclinic solution ; discrete Hamiltonian system ; critical point ; Clark’s theorem