局部有限图上非线性偏微分方程解的存在性  

The existence of solutions for nonlinear partial differential equations on locally finite graphs

作　　者：李雪 田雨陆 赵亮[1] LI Xue;TIAN Yulu;ZHAO Liang(School of Mathematical Sciences,Beijing Normal University,Beijing,China)

机构地区：[1]北京师范大学数学科学学院,北京

出　　处：《北京师范大学学报(自然科学版)》2024年第6期791-798,共8页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12271039);北京师范大学数学与复杂系统教育部重点实验室开放课题资助项目(K202303)。

摘　　要：运用从局部到全局的变分方法,将二阶方程的研究结果推广至高阶方程,并证明了局部有限图上高阶Schrödinger方程和Kazdan-Warner方程解的存在性;运用Nehari流形与高维格点图重排理论,证明了一类非线性偏微分方程重排解的存在性,并将约束变分问题的研究结果推广至无约束变分问题.In this paper,the variational method from local to global is used to generate results of second-order equations to higher-order equations,the existence of solutions for the higher-order Schrödinger equation and Kazdan-Warner equation on locally finite graphs is proved.The existence of rearrangement solutions for a class of nonlinear partial differential equations is proved using the Nehari manifold and rearrangement theory on higher-dimensional lattice graphs.Results of constrained variational problems are generalized to unconstrained variational problems.

关 键 词：局部有限图 高阶偏微分方程 变分法 格点图 Schwarz重排 

分 类 号：O175.29[理学—数学]