一类非局部问题解的存在性  

Existence of solutions for a class of nonlocal problems

作　　者：刘丽娟 LIU Li-juan(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《西南民族大学学报（自然科学版）》2021年第6期662-664,共3页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：山西省高等学校科技创新项目(2019L0783)。

摘　　要：通过变分的方法获得了一类带线性项的非局部问题解的存在性.首先得到了该问题的能量泛函并证明其具有山路引理的几何结构,接着利用反证法及其他相关知识证明了能量泛函满足(PS)条件,从而表明能量泛函存在非平凡的临界点,即证明了该问题至少存在一个解,此内容充实了非局部问题解的存在性理论.In this paper,we study the existence of solutions for a class of nonlocal problems with linear term by using variational methods.Firstly,we obtain the energy functional of the problem and prove it satisfies mountain pass geometry.Then,we show that the(PS)sequence of the energy functional contains a strong convergent sequence by contradiction and other related knowledge,which indicates that the energy functional has nontrivial critical points.Thus,we prove that the problem has at least one solution.The above results enrich the theories of solutions for nonlocal problems.

关 键 词：非局部问题 山路引理 (PS)条件 

分 类 号：O176.3[理学—数学]