具有消失位势的Schrödinger-Poisson系统的可解性  

The solvability of critical Schrödinger-Poisson systems in volving vanishing potential

作　　者：李文敏 张家锋 LI Wenmin;ZHANG Jiafeng(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《延边大学学报（自然科学版）》2023年第3期195-202,共8页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金(11861021);贵州民族大学自然科学研究项目(GZMUZK[2022]YB23)。

摘　　要：利用山路引理、Hölder不等式、嵌入不等式和估值等,研究了一类含临界非局部项且位势在无穷远处消失的Schrödinger-Poisson系统的非平凡解的存在性.首先利用嵌入不等式证明了泛函具有紧性,然后利用截断函数对泛函进行了估值,最后用变分方法证明了该系统至少有一个非平凡解.所得结果丰富了椭圆型方程解的相关理论.The existence of nontrivial solutions for a class of Schrödinger-Poisson systems containing critical nonlocal terms and vanishing potential at infinity was investigated by using the Mountain Pass Lemma,Hölder's inequality,embedding inequality and valuation.Firstly,we prove that the functional has tightness by using the embedding inequality,then the valuation of the functional is performed using the cut-off function,and finally we prove that there is at least one nontrivial solution of the system by variational method.The results of this paper enrich the theory of solutions of elliptic type equations.

关 键 词：Schrödinger-Poisson系统 变分方法 截断函数 消失位势 

分 类 号：O177.91[理学—数学]