HOMOCLINIC SOLUTIONS NEAR THE ORIGIN FOR A CLASS OF FIRST ORDER HAMILTONIAN SYSTEMS  

作　　者：张清业 刘春根 Qingye ZHANG;Chungen LIU(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang,330022,China;School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China)

机构地区：[1]School of Mathematics and Statistics,Jiangxi Normal University,Nanchang,330022,China [2]School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China

出　　处：《Acta Mathematica Scientia》2023年第3期1195-1210,共16页数学物理学报（B辑英文版）

基　　金：The first author was supported by the National Natural Science Foundation of China(11761036,11201196);the Natural Science Foundation of Jiangxi Province(20171BAB211002);The second author was supported by the National Natural Science Foundation of China(11790271,12171108);the Guangdong Basic and Applied basic Research Foundation(2020A1515011019);the Innovation and Development Project of Guangzhou University;the Nankai Zhide Foundation。

摘　　要：In this paper,we study the existence of infinitely many homoclinic solutions for a class of first order Hamiltonian systems ż=J H_(z)(t,z),where the Hamiltonian function H possesses the form H(t,z)=1/2L(t)z⋅z+G(t,z),and G(t,z)is only locally defined near the origin with respect to z.Under some mild conditions on L and G,we show that the existence of a sequence of homoclinic solutions is actually a local phenomenon in some sense,which is essentially forced by the subquadraticity of G near the origin with respect to z.

关 键 词：Hamiltonian systems homoclinic solutions variational method 

分 类 号：O175[理学—数学]