具有Choquard项的分数阶Kirchhoff型方程解  

Solutions to Fractional Kirchhoff-Type Equations with Choquard Term

作　　者：于雪 桑彦彬 韩志玲 YU Xue;SANG Yanbin;HAN Zhiling(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,太原030051

出　　处：《吉林大学学报（理学版）》2022年第6期1251-1258,共8页Journal of Jilin University:Science Edition

基　　金：山西省基础研究计划项目(批准号:202103021224198);山西省高等学校青年科研人员培育计划;中北大学科技创新研究团队项目(批准号:TD201901)。

摘　　要：考虑分数阶Choquard型Kirchhoff临界问题微分方程解的存在性.首先,引入Hardy-Littlewood-Sobolev嵌入定理,并结合Nehari流形方法及与问题相关的能量泛函纤维映射,证明该方程在参数λ足够小时非平凡解的存在性;其次,利用Ekeland变分原理得到泛函具有(PS)序列,再选取适当的参数λ,结合截断方法和山路引理证明其紧性条件成立;最后,利用分数阶的集中紧性原理建立该方程非平凡解的存在性.We considered the existence of solutions of differential equations for fractional Choquard type Kirchhoff critical problems. Firstly, Hardy-Littlewood-Sobolev embedding theorem was introduced, and combined with Nehari manifold method and fibbing maps of energy functional related to the problem, the existence of nontrivial solution of the equation was proved when the parameter λ was small enough. Secondly, the functional had(PS) sequence was obtained by Ekeland variational principle, and then the appropriate parameter λ was selected. Combined with the truncation method and mountain pass theorem, the compactness condition was proved to be true. Finally, the existence of nontrivial solutions of the above equations was established by using the fractional concentration-compactness principle.

关 键 词：Choquard方程 分数阶 临界指数 Hardy-Littlewood-Sobolev不等式 非平凡解 

分 类 号：O175.8[理学—数学]