双非局部Kirchhoff-Schrödinger-Poisson系统多重正解  

Multiple Positive Solutions for a Binonlocal Kirchhoff-Schrödinger-Poisson System

作　　者：田乖启 武玲玲 朱怡颖 TIAN Guai-qi;WU Ling-ling;ZHU Yi-ying(School of Sciences,Guizhou University of Engineering Science,Bijie,Guizhou551700,China;School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang,Guizhou550025,China)

机构地区：[1]贵州工程应用技术学院理学院,贵州毕节551700 [2]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《贵州工程应用技术学院学报》2024年第3期9-15,共7页Journal of Guizhou University Of Engineering Science

基　　金：毕节市科技局项目“Heisenberg群上的奇异次椭圆Schrödinger-Poisson方程组解的性质研究”,项目编号:毕科联合[2023]26号。

摘　　要：研究了具有奇异和双非局部的Kirchhoff-Schrödinger-Poisson系统。将“扰动”技巧用以解决带奇异项问题所对应泛函在零点处不可微的难点,应用Ekeland变分原理和山路引理得到该问题对应的扰动泛函存在局部极小和山路型的临界点,通过估计序列有一致的下界并对扰动取极限后得到两个正解的存在性。In this paper,we consider the existence of positive solution to the Kirchhoff-Schrödinger-Poisson system with singularity and binonlocal,we will perturbation technique is use to solve the problem that the functional with singular term cannot be differentiable at zero.Applying the Ekeland variational principal and mountain pass lemma,the perturbation functional corresponding to this problem has a local minimum and critical point of the mountain path type.The existence of two positive solutions is obtained by estimating the sequence with a consistent lower bound and taking the limit of perturbation.

关 键 词：Kirchhoff-Schrödinger-Poisson系统 双非局部问题 变分方法 扰动方法 

分 类 号：O177.91[理学—数学]