带有凹凸非线性项的Choquard方程的非平凡解  

Nontrivial solutions for a nonlinear Choquard equations with concave-convex nonlinearities

作　　者：李聪 鲁一宪 王玉凤 LI Cong;LU Yixian;WANG Yufeng(School of Mathematical Sciences,Qufu Normal University,273165,Qufu;Yantai First Vocational Secondary Specialized School,264001,Yantai,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,曲阜市273165 [2]烟台第一职业中等专业学校,山东省烟台市264001

出　　处：《曲阜师范大学学报（自然科学版）》2021年第2期35-43,共9页Journal of Qufu Normal University(Natural Science)

摘　　要：研究带有凹凸非线性项的Choquard方程:-Δu+u=(I_(α)*|u|^(p))|u|^(p-2)u+μg(x,u)+λf(x,u),u∈H_(0)^(1)(Ω),其中Iα是里斯位势,Ω是R^(N)中的有界光滑区域,μ是参数,λ>0.通过变分法证明当p∈(N+α/N,N+α/(N-2))+(N≥1),α∈(0,N)及非线性扰动满足一些结构性假设时解的存在性.In this paper,the nonlinear Choquard equation with the concave-convex nonlinearities-Δu+u=(I_(α)*|u|^(p))|u|^(p-2)u+μg(x,u)+λf(x,u),u∈H_(0)^1(1)(Ω)is considered,where I_(α)is a Riesz potential,Ωis a bounded smooth domain in R^(N),μis a parameter andλ>0.The existence of solutions by variational methods when p∈(N+α/N,N+α/(N-2))+,N≥1,α∈(0,N)and the nonlinear perturbation satisfies some structural assumptions is proved.

关 键 词：凹凸非线性项 山路定理 喷泉定理 Hardy-Littlewood-Sobolev不等式 

分 类 号：O175.25[理学—数学]