Homoclinic Solutions for a Class of Perturbed Fractional Hamiltonian Systems with Subquadratic Conditions  

作　　者：Ying LUO Fei GUO Yan LIU 

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》2024年第5期1177-1196,共20页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.12171355);Elite Scholar Program in Tianjin University,P.R.China。

摘　　要：In this paper,we consider the following perturbed fractional Hamiltonian systems{tD_(∞)^(α)(_(-∞)D_(t)^(α)u(t))+L(t)u(t)=■_(u)W(t,u(t))+■(u)G(t,u(t)),t∈R,u∈H^(α)(R,R^(N)),whereα∈(1/2,1],L∈C(R,R^(N×N))is symmetric and not necessarily required to be positive definite,W∈C1(R×R^(N,R))is locally subquadratic and locally even near the origin,and perturbed term G∈C1(R×R^(N,R))maybe has no parity in u.Utilizing the perturbed method improved by the authors,a sequence of nontrivial homo clinic solutions is obtained,which generalizes previous results.

关 键 词：Perturbed fractional Hamiltonian systems subquadratic condition perturbed method homoclinic solutions MULTIPLICITY 

分 类 号：O175[理学—数学]