Multiplicity of Homoclinic Solutions for Second Order Hamiltonian Systems with Local Conditions at the Origin  

作　　者：Peng LIU Fei GUO 

机构地区：[1]School of Mathematics,Tianjin University,Tianjin 300354,P.R.China [2]Tianjin Key Laboratory of Brain-Inspired Intelligence Technology,Tianjin 300354,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第4期735-744,共10页数学学报（英文版）

基　　金：National Natural Science Foundation of China(Grant No.10901118);Elite Scholar Program in Tianjin University,P.R.China。

摘　　要：In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.

关 键 词：Second order non-autonomous Hamiltonian systems Homoclinic solutions MULTIPLICITY new symmetric mountain pass lemma 

分 类 号：O175[理学—数学]