一类非线性四阶p-拉普拉斯型方程的弱解存在性  

A Class of Weak Solution Existence Problems for Nonlinear Fourth-order p-Laplace Equations

作　　者：张舒柳 梁波 ZHANG Shuliu;LIANG Bo(School of Science,Dalian Jiaotong University,Dalian Liaoning,116028;School of Mathematices and Finance,Chuzhou University,Chuzhou Anhui,239000)

机构地区：[1]大连交通大学理学院,辽宁大连116028 [2]滁州学院数学与金融学院,安徽滁州239000

出　　处：《山西大同大学学报（自然科学版）》2024年第5期27-30,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：滁州学院启动基金[2024];辽宁省教育厅高校科研项目资助[LJKMZ20220832]。

摘　　要：利用极小元法对一类非线性四阶p-Laplace方程进行求解,其中极小元法的基本内容是确定微分方程对应泛函的极小元,并由此证明微分方程弱解存在性。首先根据已知的微分方程在分部积分意义下对应的函数构造泛函,且极小元处的方程满足弱解的定义,其次将弱解存在性问题转化为方程对应泛函极小元存在性问题,最后证明了方程弱解的唯一性,最终得出结论,存在唯一弱解满足此类非线性四阶p-Laplace方程。In this paper,the minimal element method is used to solve a class of nonlinear fourth-order p-Laplace equations.The basic content of the minimal element method is to determine the minimal element of the corresponding functional of the differential equation,and prove the existence of the weak solution of the differential equation by the existence of the minimal element.In this paper,a functional is first constructed according to the function corresponding to the differential equation in the sense of integral by parts,and the equation at the functional minimum element satisfies the definition of weak solution.Secondly,the existence problem of the weak solution is transformed into the existence problem of the equation corresponding to the functional minimal element,and the existence of the weak solution is proved,the only weak solution satisfies such nonlinear fourth-order p-Laplace equations.

关 键 词：四阶p-Laplace方程 极小元 弱解 存在性 

分 类 号：O175.2[理学—数学]