一类具有变号位势的非局部问题的基态解  

Ground state solution for a class of nonlocal problems with sign-changing potential

作　　者：李盼 储昌木 LI Pan;CHU Changmu(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,贵州贵阳550025

出　　处：《高师理科学刊》2024年第12期6-9,共4页Journal of Science of Teachers'College and University

基　　金：国家自然科学基金项目(11861021)。

摘　　要：利用约束变分法,研究了有界区域上一类具有变号位势的非局部问题的基态解,克服方程中非局部项和非线性项带来的求解困扰,证明了在一定条件下能量泛函在Nehari流形上的极小化序列有界,并有一个极小元,该方程至少存在一个基态解.The ground state solutions for a class of nonlocal problems with a sign-changing potential was studied by using constraint variational methods on bounded domain.The solving difficulties caused by nonlocal term and nonlinear term in the equation were overcome,and it has been proven that under certain conditions,the minimization sequence of the energy functional on the Nehari manifold is bounded and has a minimum element,this equation has at least one ground state solution.

关 键 词：非局部问题 变号位势 约束变分法 基态解 

分 类 号：O177.91[理学—数学]