RN中一类非局部问题基态解的存在性  

Existence of ground state solutions for a class of nonlocal problem in RN

作　　者：董安祺 魏公明[1] DONG Anqi;WEI Gongming(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2023年第3期253-259,共7页Journal of University of Shanghai For Science and Technology

摘　　要：利用变分方法研究了一类RN上带有非局部项的分数阶椭圆型偏微分方程基态解的存在性。首先证明了对应泛函在Nehari流形上强制且下有界,因而得到有界极小化序列的存在性,其次应用Ekeland变分原理证明该序列是(PS)c序列,并且结合假设条件证明泛函满足(PS)c条件,最终得到该类方程基态解的存在性。The existence of ground state solutions for a class of fractional elliptic partial differential equations with nonlocal terms by variational methods was investigated.Firstly,it was shown that the functional was coercive and bounded from below Nehari manifold,and thus there existed a sequence of bounded miniaturization.Secondly,it was proved that the sequence was a(PS)sequence by Ekeland's principle.In addition,the functional was proved to satisfy the(PS)c condition in combination with the assumptions.Finally,the existence of the base state solution of this class of problems was obtained.

关 键 词：KIRCHHOFF方程 分数阶算子 基态解 

分 类 号：O175.29[理学—数学]