一类Kirchhoff-Choquard型问题正基态解的存在性  

Existence of Positive Ground State Solutions for a Class of Kirchhoff-Choquard Type Problems

作　　者：蔚艳 桑彦彬 YU Yan;SANG Yanbin(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《山西大学学报（自然科学版）》2023年第6期1262-1269,共8页Journal of Shanxi University(Natural Science Edition)

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

摘　　要：本文研究了一类Kirchhoff-Choquard型问题正基态解的存在性。首先,证明了能量泛函具有山路几何结构;其次,通过构造的唯一解的辅助函数证明了能量泛函具有收敛子列;在参数m和q选取合适的范围的情况下,借助积分式和截断函数估计山路水平值。最后,利用山路引理得到了该问题正解的存在性。进一步,结合Nehari流形方法得到了该问题正基态解的存在性。We studied the existence of positive ground state solutions for a class of Kirchhoff-Choquard type problems.Firstly,we proved that the energy functional possessed mountain pass geometry.Secondly,we proved that the energy functional had convergent subsequence by constructing the auxiliary function of unique solution.When parameters m and q were selected in appropriate ranges,the mountain pass level value was estimated using integral formula and truncation function.Finally,the existence of positive solutions for this problem was established using Mountain Pass Lemma.Furthermore,the existence of positive ground state solutions for this problem was obtained by combining Nehari manifold method.

关 键 词：Kirchhoff-Choquard型问题 山路引理 NEHARI流形 正基态解 

分 类 号：O175[理学—数学]